[1] M., Abramowitz and I. A., Stegun. Handbook of Mathematical Functions. Dover, New York, 1971.(450)Google Scholar

[2] M. J., Adams and B. L., Shader. A construction for (t,m,s)-nets in base q. SIAM J. Discrete Math., 10:460–468, 1997. (256)Google Scholar

[3] I. A., Antonov and V. M., Saleev. An effective method for the computation of XPT-sequences. Zh. Vychisl. Mat. iMat. Fiz., 19:243–245, 1979. (In Russian.) (267)Google Scholar

[4] N., Aronszajn. Theory of reproducing kernels. Trans. Amer. Math. Soc., 68:337–404, 1950. (21, 22, 29, 36, 38)Google Scholar

[5] E. I., Atanassov. Efficient CPU-specific algorithm for generating the generalized Faure sequences. In Large-scale scientific computing, Lect. Notes Comput. Sci. 2907, pp. 121-127. Springer, Berlin, 2004. (267)Google Scholar

[6] E. I., Atanassov. On the discrepancy of the Halton sequences. Math. Balkanica (N.S.), 18:15–32, 2004. (74, 75)Google Scholar

[7] J., Baldeaux and J., Dick. QMC rules of arbitrary high order: Reproducing kernel Hilbert space approach. Constr. Approx., 30:495–527, 2009. (481, 484, 492)Google Scholar

[8] J., Baldeaux, J., Dick, G., Greslehner and F., Pillichshammer. Construction algorithms for generalized polynomial lattice rules. Submitted, 2009. (507)Google Scholar

[9] J., Baldeaux, J., Dick and F., Pillichshammer. Duality theory and propagation rules for generalized nets. Submitted, 2009. (286)Google Scholar

[10] J., Beck. A two-dimensional van Aardenne Ehrenfest theorem in irregularities of distribution. Compos. Math., 72:269–339, 1989. (66)Google Scholar

[11] J., Beck and Chen, W. W. L.. Irregularities of distribution. Cambridge University Press, Cambridge, 1987. (61)Google Scholar

[12] R., Béjian. Minoration de la discrépance d'une suite quelconque sur T. Acta Arith., 41:185–202, 1982. (66)Google Scholar

[13] R., Béjian and H., Faure. Discrépance de la suite de van der Corput. C. R. Acad. Sci. Paris Sér. A-B, 285:313–316, 1977. (82)Google Scholar

[14] J., Bierbrauer, Y., Edel and W. Ch., Schmid. Coding-theoretic constructions for (t, m, s)-nets and ordered orthogonal arrays. J. Combin. Des., 10:403–418, 2002. (242, 256, 286, 344)Google Scholar

[15] D., Bilyk and M. T., Lacey. On the small ball inequality in three dimensions. Duke Math. J., 143:81–115, 2008. (67)Google Scholar

[16] D., Bilyk, M. T., Lacey and A., Vagharshakyan. On the small ball inequality in all dimensions. J. Funct. Anal., 254:2470–2502, 2008. (67)Google Scholar

[17] T., Blackmore and G. H., Norton. Matrix-product codes over Fq. Appl. Algebra Eng. Comm. Comput., 12:477–500, 2001. (288, 289)Google Scholar

[18] P., Bratley and B. L., Fox. Algorithm 659: Implementing Sobol's quasirandom sequence generator. ACM Trans. Math. Softw., 14:88–100, 1988. (267)Google Scholar

[19] P., Bratley, B. L., Fox and H., Niederreiter. Implementation and tests of low-discrepancy sequences. ACM Trans. Model. Comput. Simul., 2:195–213, 1992. (268)Google Scholar

[20] H., Chaix and H., Faure. Discrépance et diaphonie en dimension un. Acta Arith., 63:103–141, 1993. (In French.) (180)Google Scholar

[21] W. W., L.|Chen. On irregularities of point distribution. Mathematika, 27:153–170, 1980. (66)Google Scholar

[22] W. W., L.|Chen and M. M., Skriganov. Explicit constructions in the classical mean squares problem in irregularities of point distribution. J. Reine Angew. Math., 545:67–95, 2002. (xii, 66, 167, 180, 509, 510, 519, 531, 533)Google Scholar

[23] W. W., L.|Chen and M. M., Skriganov. Orthogonality and digit shifts in the classical mean squares problem in irregularities of point distribution. In Diophantine Approximation: Festschrift for Wolfgang Schmidt, pp. 141-159. Springer, Berlin, 2008. (510)Google Scholar

[24] K. L., Chung. A course in probability theory. Academic Press (a subsidiary of Harcourt Brace Jovanovich, Publishers), New York, London, second edition, 1974, vol. 21 of Probability and Mathematical Statistics. (398)

[25] J. W., Cooley and J. W., Tukey. An algorithm for the machine calculation of complex Fourier series. Math. Comp., 19:297–301, 1965. (327, 328)Google Scholar

[26] R., Cools, F. Y., Kuo and D., Nuyens. Constructing embedded lattice rules for multivariable integration. SIAM J. Sci. Comput., 28:2162–2188, 2006. (337)Google Scholar

[27] L. L., Cristea, J., Dick, G., Leobacher and F., Pillichshammer. The tent transformation can improve the convergence rate of quasi-Monte Carlo algorithms using digital nets. Numer. Math., 105:413–455, 2007. (xii, 424)Google Scholar

[28] L. L., Cristea, J., Dick and F., Pillichshammer. On the mean square weighted L2 discrepancy of randomized digital nets in prime base. J. Complexity, 22:605–629, 2006. (510, 537, 558)Google Scholar

[29] H., Davenport. Note on irregularities of distribution. Mathematika, 3:131–135, 1956. (66, 509)Google Scholar

[30] P. J., Davis. Circulant matrices. John Wiley & Sons, New York, Chichester, Brisbane, 1979. (326)Google Scholar

[31] N. G., de Bruijn and K. A., Post. A remark on uniformly distributed sequences and Riemann integrability. Nederl. Akad. Wetensch. Proc. Ser. A 71 = Indag. Math., 30:149–150, 1968. (48)Google Scholar

[32] L., de Clerck. A method for exact calculation of the star discrepancy of plane sets applied to the sequences of Hammersley. Monatsh. Math., 101:261–278, 1986. (83)Google Scholar

[33] J., Dick. On the convergence rate of the component-by-component construction of good lattice rules. J. Complexity, 20:493–522, 2004. (390)Google Scholar

[34] J., Dick. The construction of extensible polynomial lattice rules with small weighted star discrepancy. Math. Comp., 76:2077–2085, 2007. (335)Google Scholar

[35] J., Dick. Explicit constructions of quasi-Monte Carlo rules for the numerical integration of high dimensional periodic functions. SIAM J. Numer. Anal., 45:2141–2176, 2007. (xii, 435, 464, 465, 471, 472, 474, 475, 481, 484, 493)Google Scholar

[36] J., Dick. Walsh spaces containing smooth functions and quasi-Monte Carlo rules of arbitrary high order. SIAM J. Numer. Anal., 46:1519–1553, 2008. (xii, 17, 34, 437, 440, 441, 446, 465, 471, 472, 474, 475, 481, 488, 571)Google Scholar

[37] J., Dick. On quasi-Monte Carlo rules achieving higher order convergence. In Monte Carlo and quasi-Monte Carlo methods 2008, pp. 73-96. Springer, Berlin, 2009. (474)Google Scholar

[38] J., Dick. The decay of the walsh coefficients of smooth functions. Bull. Austral. Math. Soc., 80:430–453, 2009. (434, 463)Google Scholar

[39] J., Dick and J., Baldeaux. Equidistribution properties of generalized nets and sequences. In Monte Carlo and quasi-Monte Carlo methods 2008, pp. 305-322. Springer, Berlin, 2009. (475, 476, 478, 481)Google Scholar

[40] J., Dick and P., Kritzer. Star discrepancy estimates for digital (t, m, 2)-nets and digital (t, 2)-sequences over ℤ2. Acta Math. Hungar., 109:239–254, 2005. (180)Google Scholar

[41] J., Dick and P., Kritzer. A best possible upper bound on the star discrepancy of (t, m, 2)-nets. Monte Carlo Methods Appl., 12:1–17, 2006. (181, 184)Google Scholar

[42] J., Dick and P., Kritzer. Duality theory and propagation rules for generalized digital nets. Math. Comp., 79:993–1017, 2010. (473, 474)Google Scholar

[43] J., Dick, P., Kritzer, G., Leobacher and F., Pillichshammer. Constructions of general polynomial lattice rules based on the weighted star discrepancy. Finite Fields Appl., 13:1045–1070, 2007. (315, 316, 317, 320, 331, 336)Google Scholar

[44] J., Dick, P., Kritzer, F., Pillichshammer and W. Ch., Schmid. On the existence of higher order polynomial lattices based on a generalized figure of merit. J. Complexity, 23:581–593, 2007. (496)Google Scholar

[45] J., Dick, F. Y., Kuo, F., Pillichshammer and I. H., Sloan. Construction algorithms for polynomial lattice rules for multivariate integration. Math. Comp., 74:1895–1921, 2005. (xii, 317)Google Scholar

[46] J., Dick, G., Leobacher and F., Pillichshammer. Construction algorithms for digital nets with low weighted star discrepancy. SIAM J. Numer. Anal., 43:76–95, 2005. (313, 324)Google Scholar

[47] J., Dick and H., Niederreiter. On the exact t-value of Niederreiter and Sobol′ sequences. J. Complexity, 24:572–581, 2008. (265)Google Scholar

[48] J., Dick and H., Niederreiter. Duality for digital sequences. J. Complexity, 25:406–414, 2009. (244, 256)Google Scholar

[49] J., Dick, H., Niederreiter and F., Pillichshammer. Weighted star discrepancy of digital nets in prime bases. In Monte Carlo and quasi-Monte Carlo methods 2004, pp. 77-96. Springer, Berlin, 2006. (180, 219, 232, 233)Google Scholar

[50] J., Dick and F., Pillichshammer. Multivariate integration in weighted Hilbert spaces based on Walsh functions and weighted Sobolev spaces. J. Complexity, 21:149–195, 2005. (23, 43, 44, 364, 392, 393)Google Scholar

[51] J., Dick and F., Pillichshammer. On the mean square weighted L2 discrepancy of randomized digital (t, m, s)-nets over ℤ2. Acta Arith., 117:371-403, 2005. (510, 537, 557)Google Scholar

[52] J., Dick and F., Pillichshammer. Strong tractability of multivariate integration of arbitrary high order using digitally shifted polynomial lattice rules. J. Complexity, 23:436–453, 2007. (493, 499)Google Scholar

[53] J., Dick, F., Pillichshammer and B. J., Waterhouse. The construction of good extensible rank-1 lattices. Math. Comp., 77:2345–2373, 2008. (335, 337)Google Scholar

[54] J., Dick, I. H., Sloan, X., Wang and H., Woźniakowski. Liberating the weights. J. Complexity, 20:593–623, 2004. (39, 368)Google Scholar

[55] B., Doerr and M., Gnewuch. Construction of low-discrepancy point sets of small size by bracketing covers and dependent randomized rounding. In Monte Carlo and quasi-Monte Carlo methods 2006, pp. 299-312. Springer, Berlin, 2007. (92)Google Scholar

[56] B., Doerr, M., Gnewuch, P., Kritzer and F., Pillichshammer. Component-by-component construction of low-discrepancy point sets of small size. Monte Carlo Meth. Appl., 14:129–149, 2008. (92)Google Scholar

[57] B., Doerr, M., Gnewuch and A., Srivastav. Bounds and constructions for the star discrepancy via 5-covers. J. Complexity, 21:691–709, 2005. (90, 92, 106)Google Scholar

[58] B., Doerr, M., Gnewuch and M., Wahlstrom. Implementation of a component-by-component algorithm to generate small low-discrepancy samples. In Monte Carlo and quasi-Monte Carlo methods 2008, pp. 323-338. Springer, Berlin, 2009. (92)Google Scholar

[59] B., Doerr, M., Gnewuch and M., Wahlstrom. Algorithmic construction of low-discrepancy point sets via dependent randomized rounding. J. Complexity, to appear, 2010. (92)Google Scholar

[60] M., Drmota, G., Larcher and F., Pillichshammer. Precise distribution properties of the van der Corput sequence and related sequences. Manuscripta Math., 118:11–41, 2005. (82)Google Scholar

[61] M., Drmota and R. F., Tichy. Sequences, Discrepancies and Applications. Springer, Berlin, 1997. (xi, 46, 50, 60, 68, 90)Google Scholar

[62] Y., Edel and J., Bierbrauer. Construction of digital nets from BCH-codes. In Monte Carlo and quasi-Monte Carlo methods 1996 (Salzburg), vol. 127 of Lecture notes in statistics, pp. 221-231. Springer, New York, 1998. (256)Google Scholar

[63] Y., Edel and J., Bierbrauer. Families of ternary (t, m, s)-nets related to BCH-codes. Monatsh. Math., 132:99–103, 2001. (256)Google Scholar

[64] P., Erdős and P., Turán. On a problem in the theory of uniform distribution. I. Indagationes Math., 10:370–378, 1948. (68)Google Scholar

[65] P., Erdős and P., Turán. On a problem in the theory of uniform distribution. II. Indagationes Math., 10:406–413, 1948. (68)Google Scholar

[66] H., Faure. Improvement of a result of H. G. Meijer on Halton sequences. Publ. du Dép. de Math. de Limoges. (In French.) 1980. (74)Google Scholar

[67] H., Faure. Discrépances de suites associées à un système de numération (en dimension un). Bull. Soc. Math. France, 109:143–182, 1981. (In French.) (82)Google Scholar

[68] H., Faure. Discrepance de suites associées à un système de numération (en dimension s). Acta Arith., 41:337–351, 1982. (In French.) (xi, xii, 108, 132, 180, 263, 267)Google Scholar

[69] H., Faure. On the star-discrepancy of generalized Hammersley sequences in two dimensions. Monatsh. Math., 101:291–300, 1986. (83)Google Scholar

[70] H., Faure. Good permutations for extreme discrepancy. J. Number Theory, 42:47–56, 1992. (82)Google Scholar

[71] H., Faure. Discrepancy and diaphony of digital (0, 1)-sequences in prime base. Acta Arith., 117:125–148, 2005. (82, 180)Google Scholar

[72] H., Faure. Irregularities of distribution of digital (0, 1)-sequences in prime base. Integers, 5:A7, 12 pp. (electronic), 2005. (82, 180)Google Scholar

[73] H., Faure. Van der Corput sequences towards general (0, 1)-sequences in base b. J. Theor. Nombres Bordeaux, 19:125–140, 2007. (82)Google Scholar

[74] H., Faure. Star extreme discrepancy of generalized two-dimensional Hammersley point sets. Unif. Distrib. Theory, 3:45–65, 2008. (83, 180)Google Scholar

[75] H., Faure and H., Chaix. Minoration de discrepance en dimension deux. Acta Arith., 76:149–164, 1996. (In French.) (180)Google Scholar

[76] H., Faure and F., Pillichshammer. L2 discrepancy of two-dimensional digitally shifted Hammersley point sets in base b. In Monte Carlo and quasi-Monte Carlo methods 2008, pp. 355-368. Springer, Berlin, 2009. (509)Google Scholar

[77] H., Faure and F., Pillichshammer. Lp discrepancy of generalized two-dimensional Hammersley point sets. Monatsh. Math., 158:31–61, 2009. (509)Google Scholar

[78] H., Faure, F., Pillichshammer, G., Pirsic and W. Ch., Schmid. L2 discrepancy of generalized two-dimensional Hammersley point sets scrambled with arbitrary permutations. Acta Arith., 141:395–418, 2010. (509)Google Scholar

[79] N. J., Fine. On the Walsh functions. Trans. Amer. Math. Soc., 65:372–414, 1949. (434, 436, 437, 446, 567)Google Scholar

[80] B. L., Fox. Algorithm 647: Implementation and relative efficiency of quasirandom sequence generators. ACM Trans. Math. Softw., 12:362–376, 1986. (267)Google Scholar

[81] B. L., Fox. Strategies for quasi-Monte Carlo. Kluwer Academic, Boston, MA, 1999. (1)Google Scholar

[82] K., Frank and S., Heinrich. Computing discrepancies of Smolyak quadrature rules. J. Complexity, 12:287–314, 1996. (32)Google Scholar

[83] M., Frigo and S. G., Johnson. FFTW: An adaptive software architecture for the FFT. Proc. 1998 IEEE Intl. Conf. Acoustic Speech and Signal Processing, 3:1381–1384, 1998. (327)Google Scholar

[84] K. K., Frolov. Upper bound of the discrepancy in metric Lp,2 ≤ p < ∞. Dokl. Akad. NaukSSSR, 252:805–807, 1980. (66, 509)Google Scholar

[85] P., Glasserman. Monte Carlo methods in financial engineering, vol. 53 of Applications of Mathematics (New York). Springer-Verlag, New York, 2004. (1,13)Google Scholar

[86] M., Gnewuch. Bracketing numbers for axis-parallel boxes and applications to geometric discrepancy. J. Complexity, 24:154–172, 2008. (90, 106)Google Scholar

[87] M., Gnewuch, A., Srivastav and C., Winzen. Finding optimal volume subintervals with k points and calculating the star discrepancy are NP-hard problems. J. Complexity, 25:115–127, 2009. (32)Google Scholar

[88] V. S., Grozdanov and S. S., Stoilova. On the theory of b-adic diaphony. C. R. Acad. Bulgare Sci., 54:31–34, 2001. (103)Google Scholar

[89] J. H., Halton. On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals. Numer. Math., 2:84–90, 1960. (74)Google Scholar

[90] J. H., Halton and S. K., Zaremba. The extreme and the L2 discrepancies of some plane sets. Monatsh. Math., 73:316–328, 1969. (83)Google Scholar

[91] J., Hartinger and V., Ziegler. On corner avoidance properties of random-start Halton sequences. SIAM J. Numer. Anal., 45:1109–1121, 2007. (401)Google Scholar

[92] S., Heinrich. Efficient algorithms for computing the L2 discrepancy. Math. Comp., 65:1621–1633, 1996. (32)Google Scholar

[93] S., Heinrich. Some open problems concerning the star-discrepancy. J. Complexity, 19:416–419, 2003. (92)Google Scholar

[94] S., Heinrich, F. J., Hickernell and R. X., Yue. Optimal quadrature for Haar wavelet spaces. Math. Comp., 73:259–277, 2004. (431)Google Scholar

[95] S., Heinrich, E., Novak, G., Wasilkowski and H., Wozniakowski. The inverse of the star-discrepancy depends linearly on the dimension. Acta Arith., 96:279–302, 2001. (90)Google Scholar

[96] P., Hellekalek. General discrepancy estimates: the Walsh function system. Acta Arith., 67:209–218, 1994. (68, 105)Google Scholar

[97] P., Hellekalek. On the assessment of random and quasi-random point sets. In Random and quasi-random point sets, vol. 138 of Lecture Notes in Statistics, pp. 49-108. Springer, New York, 1998. (104)Google Scholar

[98] P., Hellekalek. Digital (t, m, s)-nets and the spectral test. Acta Arith., 105:197–204, 2002. (178, 179)Google Scholar

[99] P., Hellekalek and H., Leeb. Dyadic diaphony. Acta Arith., 80:187–196, 1997. (103, 104)Google Scholar

[100] P., Hellekalek and P., Liardet. The dynamic associated with certain digital sequences. In Probability and number theory - Kanazawa 2005, Advanced studies in pure mathematics, pp. 105-131. Mathematical Society of Japan, Tokyo, 2007. (136)Google Scholar

[101] F. J., Hickernell. Quadrature error bounds with applications to lattice rules. SIAM J. Numer. Anal., 33:1995–2016, 1996. (xi)Google Scholar

[102] F. J., Hickernell. A generalized discrepancy and quadrature error bound. Math. Comp., 67:299–322, 1998. (25)Google Scholar

[103] F. J., Hickernell. Lattice rules: how well do they measure up? In Random and quasi-random point sets, vol. 138 of Lecture Notes in Statistics, pp. 109-166. Springer, New York, 1998. (44, 423)Google Scholar

[104] F. J., Hickernell. Obtaining O(N−2+ε) convergence for lattice quadrature rules. In Monte Carlo and quasi-Monte Carlo methods, 2000 (Hong Kong), pp. 274-289. Springer, Berlin, 2002. (xii, 424)Google Scholar

[105] F. J., Hickernell and H. S., Hong. Computing multivariate normal probabilities using rank-1 lattice sequences. In Scientific computing (Hong Kong, 1997), pp. 209-215. Springer, Singapore, 1997. (329)Google Scholar

[106] F. J., Hickernell, P., Kritzer, F. Y., Kuo and D., Nuyens. Weighted compound integration rules with higher order convergence for all n. Submitted, 2010. (28)Google Scholar

[107] F. J., Hickernell and H., Niederreiter. The existence of good extensible rank-1 lattices. J. Complexity, 19:286–300, 2003. (217, 222, 330)Google Scholar

[108] F. J., Hickernell and R.-X., Yue. The mean square discrepancy of scrambled (t, i)-sequences. SIAM J. Numer. Anal., 38:1089–1112, 2000. (396, 413)Google Scholar

[109] A., Hinrichs. Covering numbers, Vapnik–Červonenkis classes and bounds for the star-discrepancy. J. Complexity, 20:477–483, 2004. (90)Google Scholar

[110] A., Hinrichs, F., Pillichshammer and W. Ch., Schmid. Tractability properties of the weighted star discrepancy. J. Complexity, 24:134–143, 2008. (99, 102)Google Scholar

[111] E., Hlawka. Funktionen von beschrankter Variation in der Theorie der Gleichverteilung. Ann. Mat. PuraAppl., 54:325–333, 1961. (In German.) (xi, 33)Google Scholar

[112] E., Hlawka. Über die Diskrepanz mehrdimensionaler Folgen mod 1. Math. Z., 77:273–284, 1961. (In German.) (18, 33)Google Scholar

[113] E., Hlawka. Zur angenäherten Berechnung mehrfacher Integrale. Monatsh. Math., 66:140–151, 1962. (In German.) (84)Google Scholar

[114] L. K., Hua and Y., Wang. Applications of number theory to numerical analysis. Springer, Berlin, 1981. (xi, 74)Google Scholar

[115] S., Joe. Component by component construction of rank-1 lattice rules having O(n−1(ln(n))d) star discrepancy. In Monte Carlo and quasi-Monte Carlo methods 2002, pp. 293-298. Springer, Berlin, 2004. (85)Google Scholar

[116] S., Joe. Construction of good rank-1 lattice rules based on the weighted star discrepancy. In Monte Carlo and quasi-Monte Carlo methods 2004, pp. 181-196. Springer, Berlin, 2006. (217)Google Scholar

[117] S., Joe and F. Y., Kuo. Constructing Sobol′ sequences with better two-dimensional projections. SIAM J. Sci. Comput., 30:2635–2654, 2008. (267)Google Scholar

[118] S., Joe and I. H., Sloan. On computing the lattice rule criterion R. Math. Comp., 59:557–568, 1992. (85)Google Scholar

[119] Y., Katznelson. An introduction to harmonic analysis. Cambridge Mathematical Library. Cambridge University Press, Cambridge, third edition, 2004. (566)Google Scholar

[120] A., Keller. Myths of computer graphics. In Monte Carlo and quasi-Monte Carlo methods 2004, pp. 217-243. Springer, Berlin, 2006. (1)Google Scholar

[121] J. F., Koksma. Een algemeene stelling uit de theorie der gelijkmatige verdeeling modulo 1. Mathematica B (Zutphen), 11:7-11, 1942/43. (xi, 19, 33)Google Scholar

[122] J. F., Koksma. Some theorems on Diophantine inequalities. Scriptum no. 5, Math. Centrum Amsterdam, 1950. (68)Google Scholar

[123] N. M., Korobov. Approximate evaluation of repeated integrals. Dokl. Akad. Nauk SSSR, 124:1207–1210, 1959. (84)Google Scholar

[124] N. M., Korobov. Properties and calculation of optimal coefficients. Dokl. Akad. Nauk SSSR, 132:1009–1012, 1960. (In Russian.) (106, 306)Google Scholar

[125] P., Kritzer. Improved upper bounds on the star discrepancy of (t, m, s)-nets and (t, s)-sequences. J. Complexity, 22:336–347, 2006. (180, 183, 196)Google Scholar

[126] P., Kritzer. On the star discrepancy of digital nets and sequences in three dimensions. In Monte Carlo and quasi-Monte Carlo methods 2004, pp. 273-287. Springer, Berlin, 2006. (180)Google Scholar

[127] P., Kritzer, G., Larcher and F., Pillichshammer. A thorough analysis of the discrepancy of shifted Hammersley and van der Corput point sets. Ann. Mat. Pura Appl. (4), 186:229–250, 2007. (82)Google Scholar

[128] P., Kritzer and F., Pillichshammer. An exact formula for the L2 discrepancy of the shifted Hammersley point set. Unif. Distrib. Theory, 1:1–13, 2006. (509)Google Scholar

[129] P., Kritzer and F., Pillichshammer. Constructions of general polynomial lattices for multivariate integration. Bull. Austral. Math. Soc., 76:93–110, 2007. (384)Google Scholar

[130] L., Kuipers and H., Niederreiter. Uniform distribution ofsequences. John Wiley, New York, 1974. Reprint, Dover Publications, Mineola, NY, 2006. (xi, xii, 19, 32, 43, 46, 48, 50, 58, 61, 66, 67, 68, 73, 103, 104)Google Scholar

[131] F. Y., Kuo. Component-by-component constructions achieve the optimal rate of convergence for multivariate integration in weighted Korobov and Sobolev spaces. J. Complexity, 19:301–320, 2003. (390)Google Scholar

[132] G., Larcher. A best lower bound for good lattice points. Monatsh. Math., 104:45–51, 1987. (87)Google Scholar

[133] G., Larcher. A class of low-discrepancy point-sets and its application to numerical integration by number-theoretical methods. In Österreichisch-Ungarisch-Slowakisches Kolloquium über Zahlentheorie (Maria Trost, 1992), vol. 318 of Grazer Math. Ber., pp. 69-80. Karl-Franzens-Univ. Graz, 1993. (xii, 363)Google Scholar

[134] G., Larcher. Nets obtained from rational functions over finite fields. Acta Arith., 63:1–13, 1993. (180, 316)Google Scholar

[135] G., Larcher. On the distribution of an analog to classical Kronecker-sequences. J. Number Theory, 52:198–215, 1995. (134, 180)Google Scholar

[136] G., Larcher. A bound for the discrepancy of digital nets and its application to the analysis of certain pseudo-random number generators. Acta Arith., 83:1–15, 1998. (180, 199)Google Scholar

[137] G., Larcher. Digital point sets: analysis and application. In Random and quasi-random point sets, vol. 138 of Lecture Notes in Statistics, pp. 167-222. Springer, New York, 1998. (146, 167, 213)Google Scholar

[138] G., Larcher. On the distribution of digital sequences. In Monte Carlo and quasi-Monte Carlo methods 1996 (Salzburg), vol. 127 of Lecture notes in statistics, pp. 109-123. Springer, New York, 1998. (180, 199, 206, 227, 228)Google Scholar

[139] G., Larcher, A., Lauss, H., Niederreiter and W. Ch., Schmid. Optimal polynomials for (t, m, s)-nets and numerical integration of multivariate Walsh series. SIAM J. Numer. Anal., 33:2239–2253, 1996. (306, 309,493)Google Scholar

[140] G., Larcher and H., Niederreiter. Generalized (t, s)-sequences, Kronecker-type sequences, and diophantine approximations of formal Laurent series. Trans. Amer. Math. Soc., 347:2051–2073, 1995. (132, 180, 191, 196, 225)Google Scholar

[141] G., Larcher, H., Niederreiter and W. Ch., Schmid. Digital nets and sequences constructed over finite rings and their application to quasi-Monte Carlo integration. Monatsh. Math., 121:231–253, 1996. (125, 146, 163, 167, 211)Google Scholar

[142] G., Larcher and F., Pillichshammer. Walsh series analysis of the L2-discrepancy of symmetrisized point sets. Monatsh. Math., 132:1–18, 2001. (180, 509)Google Scholar

[143] G., Larcher and F., Pillichshammer. On the L2-discrepancy of the Sobol-Hammersley net in dimension 3. J. Complexity, 18:415–448, 2002. (180, 509)Google Scholar

[144] G., Larcher and F., Pillichshammer. Sums of distances to the nearest integer and the discrepancy of digital nets. Acta Arith., 106:379–408, 2003. (83, 180, 181)Google Scholar

[145] G., Larcher and F., Pillichshammer. Walsh series analysis of the star discrepancy of digital nets and sequences. In Monte Carlo and quasi-Monte Carlo methods 2002, pp. 315-327. Springer, Berlin, 2004. (180)Google Scholar

[146] G., Larcher, F., Pillichshammer and K., Scheicher. Weighted discrepancy and high-dimensional numerical integration. BIT, 43:123–137, 2003. (180)Google Scholar

[147] G., Larcher and W. Ch., Schmid. On the numerical integration of high-dimensional Walsh-series by quasi-Monte Carlo methods. Math. Comput. Simulation, 38:127–134, 1995. (234, 363)Google Scholar

[148] G., Larcher and C., Traunfellner. On the numerical integration of Walsh series by number-theoretic methods. Math. Comp., 63:277–291, 1994. (xii, 363)Google Scholar

[149] K. M., Lawrence. A combinatorial characterization of (t, m, s)-nets in base b. J. Combin. Des., 4:275–293, 1996. (240, 242)Google Scholar

[150] K. M., Lawrence, A., Mahalanabis, G. L., Mullen and W. Ch., Schmid. Construction of digital (t, m, s)-nets from linear codes. In Finite fields and applications (Glasgow, 1995), vol. 233 of London Mathematical Society Lecture Notes Series, pp. 189-208. Cambridge University Press, Cambridge, 1996. (253)Google Scholar

[151] P., L'Ecuyer. Quasi-Monte Carlo methods with applications in finance. Finance and Stochastics, 13:307–349, 2009. (1)Google Scholar

[152] P., L'Ecuyer and P., Hellekalek. Random number generators: selection criteria and testing. In Random and quasi-random point sets, vol. 138 of Lecture Notes in Statistics, pp. 223-265. Springer, New York, 1998. (13)Google Scholar

[153] P., L'Ecuyer and Ch., Lemieux. Recent advances in randomized quasi-Monte Carlo methods. In Modeling uncertainty, vol. 46 of International Series in Operation. Research Management Science, pp. 419-474. Kluwer Acaderic Publishers, Boston, MA, 2002. (330, 401)Google Scholar

[154] Ch., Lemieux. Monte Carlo and quasi-Monte Carlo sampling. Springer Series in Statistics. Springer, New York, 2008. (1, 13, 401)Google Scholar

[155] Ch., Lemieux and P., L'Ecuyer. Randomized polynomial lattice rules for multivariate integration and simulation. SIAM J. Sci. Comput., 24:1768–1789, 2003. (299)Google Scholar

[156] G., Leobacher and F., Pillichshammer. Bounds for the weighted Lp discrepancy and tractability of integration. J. Complexity, 19:529–547, 2003. (107)Google Scholar

[157] R., Lidl and H., Niederreiter. Introduction to finite fields and their applications. Cambridge University Press, Cambridge, first edition, 1994. (254, 255, 299)Google Scholar

[158] W.-L., Loh. On the asymptotic distribution of scrambled net quadrature. Ann. Statist., 31:1282–1324, 2003. (412)Google Scholar

[159] W. J., Martin and D. R., Stinson. Association schemes for ordered orthogonal arrays and (T, M, S)-nets. Canad. J. Math., 51:326–346, 1999. (242, 256)Google Scholar

[160] J., Matoušek. On the L2-discrepancy for anchored boxes. J. Complexity, 14:527–556, 1998. (400, 555)Google Scholar

[161] J., Matoušek. Geometric discrepancy. Springer, Berlin, 1999. (400, 432)Google Scholar

[162] J., Matoušek and J., Nešetril. Invitation to discrete mathematics. Oxford University Press, Oxford, second edition, 2009. (238)Google Scholar

[163] H. G., Meijer. The discrepancy of a g-adic sequence. Nederl. Akad. Wetensch. Proc. Ser. A 71=Indag. Math., 30:54–66, 1968. (74, 234)Google Scholar

[164] G. L., Mullen. Orthogonal hypercubes and related designs. J. Statist. Plann. Inference, 73:177–188, 1998. (239)Google Scholar

[165] G. L., Mullen and W. Ch., Schmid. An equivalence between (t, m, s)-nets and strongly orthogonal hypercubes. J. Combin. Theory Ser. A, 76:164-174, 1996. (239, 240, 243)Google Scholar

[166] G. L., Mullen and G., Whittle. Point sets with uniformity properties and orthogonal hypercubes. Monatsh. Math., 113:265–273, 1992. (239)Google Scholar

[167] H., Niederreiter. On the distribution of pseudo-random numbers generated by the linear congruential method. III. Math. Comp., 30:571–597, 1976. (221)Google Scholar

[168] H., Niederreiter. Existence of good lattice points in the sense of Hlawka. Monatsh. Math., 86:203–219, 1978. (87, 180)Google Scholar

[169] H., Niederreiter. Low-discrepancy point sets. Monatsh. Math., 102:155–167, 1986. (245)Google Scholar

[170] H., Niederreiter. Pseudozufallszahlen und die Theorie der Gleichverteilung. Österreich. Akad. Wiss. Math.-Natur. Kl. Sitzungsber. II, 195:109–138, 1986. (In German.) (xii, 68, 234)Google Scholar

[171] H., Niederreiter. Quasi-Monte Carlo methods and pseudo-random numbers. Bull. Amer. Math. Soc., 84:957–1041, 1986. (xi)Google Scholar

[172] H., Niederreiter. Point sets and sequences with small discrepancy. Monatsh. Math., 104:273–337, 1987. (xi, 108, 117, 132, 153, 180, 234, 235)Google Scholar

[173] H., Niederreiter. Low-discrepancy and low-dispersion sequences. J. Number Theory, 30:51–70, 1988. (xi, xii, 263, 264, 268)Google Scholar

[174] H., Niederreiter. A combinatorial problem for vector spaces over finite fields. Discrete Math., 96:221–228, 1991. (246)Google Scholar

[175] H., Niederreiter. Low-discrepancy point sets obtained by digital constructions over finite fields. Czechoslovak Math. J., 42:143–166, 1992. (68, 298, 302, 303)Google Scholar

[176] H., Niederreiter. Orthogonal arrays and other combinatorial aspects in the theory of uniform point distributions in unit cubes. Discrete Math., 106/107:361-367, 1992. (238, 239, 242)Google Scholar

[177] H., Niederreiter. Random number generation and quasi-Monte Carlo methods. Number 63 in CBMS-NSF Series in Applied Mathematics. SIAM, Philadelphia, 1992. (xi, 12, 13, 15, 17, 32, 34, 59, 68, 73, 74, 82, 85, 87, 88, 108, 123, 141, 146, 150, 167, 180, 181, 182, 184, 191, 192, 193, 194, 195, 197, 219, 232, 234, 264, 266, 298, 299, 302, 303, 305, 313, 315, 342)Google Scholar

[178] H., Niederreiter. Finite fields, pseudorandom numbers, and quasirandom points. In Finite fields, coding theory, and advances in communications and computing (Las Vegas, NV, 1991), vol. 141 of Lecture Notes in Pure and Applied Mathematics, pp. 375-394. Dekker, New York, 1993. (300)Google Scholar

[179] H., Niederreiter. Constructions of (t, m, s)-nets. In Monte Carlo and quasi-Monte Carlo methods 1998, pp. 70-85. Springer, Berlin, 2000. (285)Google Scholar

[180] H., Niederreiter. Algebraic function fields over finite fields. In Coding theory and cryptology (Singapore, 2001), vol. 1 of Lecture Notes Series, Institute for Mathematical. Science National University Singapore, pp. 259-282. World Scientific Publishers, River Edge, NJ, 2002. (572, 573, 574, 575, 576, 577, 581, 582)Google Scholar

[181] H., Niederreiter. Error bounds for quasi-Monte Carlo integration with uniform point sets. J. Comput. Appl. Math., 150:283–292, 2003. (15)Google Scholar

[182] H., Niederreiter. The existence of good extensible polynomial lattice rules. Monatsh. Math., 139:295–307, 2003. (330, 331)Google Scholar

[183] H., Niederreiter. Digital nets and coding theory. In Coding, cryptography and combinatorics,vol. 23 of Progr. Comput. Sci. Appl. Logic, pp. 247-257. Birkhauser, Basel, 2004. (244, 256, 344)Google Scholar

[184] H., Niederreiter. Constructions of (t, m, s)-nets and (t, i)-sequences. Finite Fields Appl., 11:578–600, 2005. (244, 253, 286, 347)Google Scholar

[185] H., Niederreiter. Nets, (t, s)-sequences and codes. In Monte Carlo and quasi-Monte Carlo methods 2006, pp. 83-100. Springer, Berlin, 2008. (256)Google Scholar

[186] H., Niederreiter and F., Özbudak. Constructions of digital nets using global function fields. Acta Arith., 105:279–302, 2002. (268)Google Scholar

[187] H., Niederreiter and F., Özbudak. Matrix-product constructions of digital nets. Finite Fields Appl., 10:464–479, 2004. (288, 289)Google Scholar

[188] H., Niederreiter and F., Pillichshammer. Construction algorithms for good extensible lattice rules. Constr. Approx., 30:361–393, 2009. (337)Google Scholar

[189] H., Niederreiter and G., Pirsic. Duality for digital nets and its applications. Acta Arith., 97:173–182, 2001. (xii, 166, 167, 244, 246, 256, 290)Google Scholar

[190] H., Niederreiter and G., Pirsic. A Kronecker product construction for digital nets. In Monte Carlo and quasi-Monte Carlo methods, 2000 (Hong Kong), pp. 396-405. Springer, Berlin, 2002. (344)Google Scholar

[191] H., Niederreiter and C. P., Xing. Low-discrepancy sequences obtained from algebraic function fields over finite fields. Acta Arith., 72:281–298, 1995. (xii)Google Scholar

[192] H., Niederreiter and C. P., Xing. Low-discrepancy sequences and global function fields with many rational places. Finite Fields Appl., 2:241–273, 1996. (120, 127, 143, 144, 275, 277, 476)Google Scholar

[193] H., Niederreiter and C. P., Xing. Quasirandom points and global function fields. In S., Cohen and H., Niederreiter, eds, Finite fields and applications, vol. 233 of London Mathematical Society Lecture Note Series, pp. 269-296, Cambridge University Press, Cambridge, 1996. (476, 552)Google Scholar

[194] H., Niederreiter and C. P., Xing. Nets, (t, s)-sequences, and algebraic geometry. In Random and quasi-random point sets, vol. 138 of Lecture Notes in Statistics, pp. 267-302. Springer, New York, 1998. (198, 251, 292, 551)Google Scholar

[195] H., Niederreiter and C. P., Xing. Rational points on curves over finite fields: theory and applications, vol. 285 of London Mathematical Society Lecture Notes Series. Cambridge University Press, Cambridge, 2001. (572)Google Scholar

[196] H., Niederreiter and C. P., Xing. Constructions of digital nets. Acta Arith., 102:189–197, 2002. (294)Google Scholar

[197] H., Niederreiter and C. P., Xing. Algebraic geometry in coding theory and cryptography. Princeton University Press, Princeton and Oxford, 2009. (268, 572)Google Scholar

[198] E., Novak. Numerische Verfahren fur hochdimensionale Probleme und der Fluch der Dimension. Jahresber. Deutsch. Math.-Verein., 101:151–177, 1999. (In German.) (89)Google Scholar

[199] E., Novak and H., Woźniakowski. When are integration and discrepancy tractable? In Foundations ofcomputational mathematics (Oxford, 1999), vol. 284 of London Mathematical Society Lecture Notes Series, pp. 211-266. Cambridge University Press, Cambridge, 2001. (94, 103)Google Scholar

[200] E., Novak and H., Woźniakowski. Tractability of Multivariate Problems. Volume I: Linear Information. European Mathematical Society Publishing House, Zurich, 2008. (34, 94, 103, 368)Google Scholar

[201] E., Novak and H., Woźniakowski. L2 discrepancy and multivariate integration. In Analytic number theory, pp. 359-388. Cambridge University Press, Cambridge, 2009. (94, 103)Google Scholar

[202] E., Novak and H., Woźniakowski. Tractability of multivariate problems. Volume II: standard information for functionals. European Mathematical Society Publishing House, Zurich, 2010. (34, 92, 94, 103)Google Scholar

[203] D., Nuyens. Fast construction of good lattice rules. PhD thesis, Departement Computerwetenschappen, Katholieke Universiteit Leuven, 2007. (323)Google Scholar

[204] D., Nuyens and R., Cools. Fast algorithms for component-by-component construction of rank-1 lattice rules in shift-invariant reproducing kernel Hilbert spaces. Math. Comp., 75:903–920, 2006. (322, 325)Google Scholar

[205] D., Nuyens and R., Cools. Fast component-by-component construction, a reprise for different kernels. In Monte Carlo and quasi-Monte Carlo methods 2004, pp. 373-387. Springer, Berlin, 2006. (322, 323, 325)Google Scholar

[206] A. B., Owen. Randomly permuted (t, m, s)-nets and (t, s)-sequences. In Monte Carlo and quasi-Monte Carlo Methods in scientific computing (Las Vegas, NV, 1994), vol. 106 of Lecture Notes in Statistics, pp. 299-317. Springer, New York, 1995. (xii, 243, 396, 397, 400)Google Scholar

[207] A. B., Owen. Monte Carlo variance of scrambled net quadrature. SIAM J. Numer. Anal., 34:1884–1910, 1997. (xii, xiii, 396, 401, 402, 408, 409, 412)Google Scholar

[208] A. B., Owen. Scrambled net variance for integrals of smooth functions. Ann. Statist., 25:1541–1562, 1997. (396,424, 425)Google Scholar

[209] A. B., Owen. Monte Carlo, quasi-Monte Carlo, and randomized quasi-Monte Carlo. In Monte Carlo and quasi-Monte Carlo methods 1998, pp. 86-97, Springer, Berlin, 2000. (xii, 396)Google Scholar

[210] A. B., Owen. Quasi-Monte Carlo for integrands with point singularities at unknown locations. In Monte Carlo and quasi-Monte Carlo methods 2004, pp. 403-417. Springer, Berlin, 2006. (401)Google Scholar

[211] A. B., Owen. Local antithetic sampling with scrambled nets. Ann. Statist., 36:2319–2343, 2008. (401, 424, 425, 431)Google Scholar

[212] F., Pillichshammer. On the Lp -discrepancy of the Hammersley point set. Monatsh. Math., 136:67–79, 2002. (180)Google Scholar

[213] F., Pillichshammer. Improved upper bounds for the star discrepancy of digital nets in dimension 3. Acta Arith., 108:167–189, 2003. (180, 182)Google Scholar

[214] F., Pillichshammer and G., Pirsic. Discrepancy of hyperplane nets and cyclic nets. In Monte Carlo and quasi-Monte Carlo methods 2008, Berlin, 2009. Springer. (355)Google Scholar

[215] F., Pillichshammer and G., Pirsic. The quality parameter of cyclic nets and hyperplane nets. Unif. Distrib. Theory, 4:69–79, 2009. (352, 353)Google Scholar

[216] G., Pirsic. Schnell konvergierende Walshreihen über Gruppen. Master's thesis, Institute for Mathematics, University of Salzburg, (In German.) 1995. (559)Google Scholar

[217] G., Pirsic. Embedding theorems and numerical integration of Walsh series over groups. PhD thesis, Institute for Mathematics, University of Salzburg, 1997. (127, 446)Google Scholar

[218] G., Pirsic. Base changes for (t, m, s)-nets and related sequences. Österreich. Akad. Wiss. Math.-Natur. Kl. Sitzungsber. II, 208:115-122 (2000), 1999. (127)Google Scholar

[219] G., Pirsic. A software implementation of Niederreiter-Xing sequences. In Monte Carlo and quasi-Monte Carlo methods, 2000 (Hong Kong), pp. 434-445. Springer, Berlin, 2002. (279)Google Scholar

[220] G., Pirsic. A small taxonomy of integration node sets. Österreich. Akad. Wiss. Math.-Natur. Kl. Sitzungsber. II, 214:133-140 (2006), 2005. (349)Google Scholar

[221] G., Pirsic, J., Dick and F., Pillichshammer. Cyclic digital nets, hyperplane nets and multivariate integration in Sobolev spaces. SIAM J. Numer. Anal., 44:385–411, 2006. (166, 344, 346, 347)Google Scholar

[222] G., Pirsic and W. Ch., Schmid. Calculation of the quality parameter of digital nets and application to their construction. J. Complexity, 17:827–839, 2001. (299)Google Scholar

[223] P. D., Proĭnov. Symmetrization of the van der Corput generalized sequences. Proc. Jap. Acad. Ser. A Math. Sci., 64:159–162, 1988. (509)Google Scholar

[224] C. M., Rader. Discrete Fourier transforms when the number of data samples is prime. Proc. IEEE, 5:1107–1108, 1968. (325)Google Scholar

[225] I., Radović, I. M., Sobol′ and R. F., Tichy. Quasi-Monte Carlo methods for numerical integration: comparison of different low discrepancy sequences. Monte Carlo Meth. Appl., 2:1–14, 1996. (136)Google Scholar

[226] D., Raghavarao. Constructions and combinatorial problems in design of experiments. Wiley Series in Probability and Mathematical Statistics. John Wiley & Sons Inc., New York, 1971. (242)Google Scholar

[227] M. Yu., Rosenbloom and M. A., Tsfasman. Codes in the m -metric. Problemi Peredachi Inf., 33:45–52, 1997. (245)Google Scholar

[228] K. F., Roth. On irregularities of distribution. Mathematika, 1:73–79, 1954. (xii, 60, 61, 82)Google Scholar

[229] K. F., Roth. On irregularities of distribution III. Acta Arith., 35:373–384, 1979. (66, 509)Google Scholar

[230] K. F., Roth. On irregularities of distribution IV. Acta Arith., 37:67–75, 1980. (66, 509)Google Scholar

[231] J., Sándor, D. S., Mitrinović and B., Crstici. Handbook of number theory. I.Springer, Dordrecht, 2006. Second printing of the 1996 original. (81)Google Scholar

[232] F., Schipp, W. R., Wade and P., Simon. Walsh series. An introduction to dyadic harmonic analysis. Adam Hilger Ltd., Bristol, 1990. (559, 567)Google Scholar

[233] W. Ch., Schmid. (t, m, s)-nets: digital construction and combinatorial aspects. PhD thesis, Institute for Mathematics, University of Salzburg, 1995. (240, 253, 286)Google Scholar

[234] W. Ch., Schmid. Shift-nets: a new class of binary digital (t, m, s)-nets. In Monte Carlo and quasi-Monte Carlo methods 1996 (Salzburg), vol. 127 of Lecture Notes in Statistics, pp. 369-381. Springer, New York, 1998. (552)Google Scholar

[235] W. Ch., Schmid. Improvements and extensions of the ‘Salzburg tables’ by using irreducible polynomials. In Monte Carlo and quasi-Monte Carlo methods 1998 (Claremont, CA), pp. 436-447. Springer, Berlin, 2000. (299, 306)Google Scholar

[236] W. Ch., Schmid and R., Wolf. Bounds for digital nets and sequences. Acta Arith., 78:377–399, 1997. (155)Google Scholar

[237] W. M., Schmidt. Irregularities of distribution VII. Acta Arith., 21:45–50, 1972. (66)Google Scholar

[238] W. M., Schmidt. Irregularities of distribution. X. In Number theory and algebra, pp. 311-329. Academic Press, New York, 1977. (66)Google Scholar

[239] R., Schuärer and W. Ch., Schmid. MinT: a database for optimal net parameters. In Monte Carlo and quasi-Monte Carlo methods 2004, pp. 457-469. Springer, Berlin, 2006. (275)Google Scholar

[240] R., Schürer and W. Ch., Schmid. MinT- New features and new results. In Monte Carlo and quasi-Monte Carlo methods 2008, pp. 171-189. Springer, Berlin, 2009. (242, 256)Google Scholar

[241] I. F., Sharygin. A lower estimate for the error of quadrature formulas for certain classes of functions. Zh. Vychisl. Mat. i Mat. Fiz., 3:370–376, 1963. (In Russian.) (468, 476, 492, 493, 504)Google Scholar

[242] V., Sinescu and S., Joe. Good lattice rules with a composite number of points based on the product weighted star discrepancy. In Monte Carlo and quasi-Monte Carlo methods 2006, pp. 645-658. Springer, Berlin, 2008. (86)Google Scholar

[243] M. M., Skriganov. Coding theory and uniform distributions. Algebra iAnaliz, 13:191–239, 2001. Translation in St. Petersburg Math. J. 13:2, 2002, 301-337. (166, 244, 256, 519, 556)Google Scholar

[244] M. M., Skriganov. Harmonic analysis on totally disconnected groups and irregularities of point distributions. J. ReineAngew. Math., 600:25–49, 2006. (66, 180, 509,510)Google Scholar

[245] I. H., Sloan and S., Joe. Lattice methods for multiple integration. Oxford University Press, New York and Oxford, 1994. (88, 298)Google Scholar

[246] I. H., Sloan, F. Y., Kuo and S., Joe. Constructing randomly shifted lattice rules in weighted Sobolev spaces. SIAM J. Numer. Anal., 40:1650–1665, 2002. (xii, 390)Google Scholar

[247] I. H., Sloan, F. Y., Kuo and S., Joe. On the step-by-step construction of quasi-Monte Carlo integration rules that achieve strong tractability error bounds in weighted Sobolev spaces. Math. Comp., 71:1609–1640, 2002. (xii, 390)Google Scholar

[248] I. H., Sloan and A. V., Reztsov. Component-by-component construction of good lattice rules. Math. Comp., 71:263–273, 2002. (85)Google Scholar

[249] I. H., Sloan and H., Woźniakowski. When are quasi-Monte Carlo algorithms efficient for high-dimensional integrals?J. Complexity, 14:1–33, 1998. (xi, 25, 34, 35, 45, 93, 94)Google Scholar

[250] I. H., Sloan and H., Woźniakowski. Tractability of multivariate integration for weighted Korobov classes. J. Complexity, 17:697–721, 2001. (44)Google Scholar

[251] I. H., Sloan and H., Woźniakowski. Tractability of integration in non-periodic and periodic weighted tensor product Hilbert spaces. J. Complexity, 18:479–499, 2002. (43, 368)Google Scholar

[252] I. M., Sobol′. Functions of many variables with rapidly convergent Haar series. Soviet Math. Dokl., 1:655–658, 1960. (xiii)Google Scholar

[253] I. M., Sobol′. Distribution of points in a cube and approximate evaluation of integrals. Ž. Vyčisl. Mat. i Mat. Fiz., 7:784–802, 1967. (xi, xii, xiii, 108, 114, 123, 132, 153, 180, 263,266)Google Scholar

[254] H., Stichtenoth. Algebraic function fields and codes. Universitext. Springer, Berlin, 1993. (572, 577, 580, 581)Google Scholar

[255] S., Tezuka. Polynomial arithmetic analogue of Halton sequences. ACM Trans. Model. Comput. Simul., 3:99–107, 1993. (266)Google Scholar

[256] S., Tezuka. Uniform random numbers: theory and practice. Kluwer International Series in Engineering and Computer Science. Kluwer, Boston, 1995. (1, 266)Google Scholar

[257] S., Tezuka and H., Faure. I -binomial scrambling of digital nets and sequences. J. Complexity, 19:744–757, 2003. (400)Google Scholar

[258] H., Triebel. Bases in function spaces, sampling, discrepancy, numerical integration. To appear, 2009. (34)Google Scholar

[259] G., Wahba. Spline models for observational data, Vol. 59 of CBMS-NSF Regional Conference Series in Applied Mathematics. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1990. (458)Google Scholar

[260] J. L., Walsh. A closed set of normal orthogonal functions. Amer. J. Math., 45:5–24, 1923. (559, 567)Google Scholar

[261] X., Wang. A constructive approach to strong tractability using quasi-Monte Carlo algorithms. J. Complexity, 18:683–701, 2002. (223)Google Scholar

[262] X., Wang. Strong tractability of multivariate integration using quasi-Monte Carlo algorithms. Math. Comp., 72:823–838, 2003. (223)Google Scholar

[263] T. T., Warnock. Computational investigations of low discrepancy point sets. In Applications of number theory to numerical analysis, pp. 319-343. Academic Press, New York 1972. (31)Google Scholar

[264] E., Weiss. Algebraic number theory. McGraw-Hill Book Co., Inc., New York, 1963. (572, 577)Google Scholar

[265] H., Weyl. Über die Gleichverteilung von Zahlen mod. Eins. Math. Ann., 77:313–352, 1916. (In German.) (xi, 47)Google Scholar

[266] H., Woźniakowski. Efficiency of quasi-Monte Carlo algorithms for high dimensional integrals. In Monte Carlo and quasi-Monte Carlo methods 1998 (Claremont, CA), pp. 114-136. Springer, Berlin, 2000. (93)Google Scholar

[267] C. P., Xing and H., Niederreiter. A construction of low-discrepancy sequences using global function fields. Acta Arith., 73:87–102, 1995. (xii, 278, 280, 281)Google Scholar

[268] C. P., Xing and H., Niederreiter. Digital nets, duality, and algebraic curves. In Monte Carlo and quasi-Monte Carlo methods 2002, pp. 155-166. Springer, Berlin, 2004. (552)Google Scholar

[269] R.-X., Yue and F. J., Hickernell. Integration and approximation based on scramble sampling in arbitrary dimensions. J. Complexity, 17:881–897, 2001. (396)Google Scholar

[270] R.-X., Yue and F. J., Hickernell. The discrepancy and gain coefficients of scrambled digital nets. J. Complexity, 18:135–151, 2002. (396, 409, 412)Google Scholar

[271] R.-X., Yue and F. J., Hickernell. Strong tractability of integration using scrambled Niederreiter points. Math. Comp., 74:1871–1893, 2005. (396, 409, 412, 425, 431)Google Scholar

[272] S. K., Zaremba. Some applications of multidimensional integration by parts. Ann. Poln. Math., 21:85–96, 1968. (18, 33)Google Scholar

[273] A., Zygmund. Trigonometric series. Cambridge University Press, Cambridge, 1959. (434)Google Scholar