[1] M., Abramowitz and I. A., Stegun. Handbook of Mathematical Functions. Dover, New York, 1971.(450)
[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)
[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)
[4] N., Aronszajn. Theory of reproducing kernels. Trans. Amer. Math. Soc., 68:337–404, 1950. (21, 22, 29, 36, 38)
[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)
[6] E. I., Atanassov. On the discrepancy of the Halton sequences. Math. Balkanica (N.S.), 18:15–32, 2004. (74, 75)
[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)
[8] J., Baldeaux, J., Dick, G., Greslehner and F., Pillichshammer. Construction algorithms for generalized polynomial lattice rules. Submitted, 2009. (507)
[9] J., Baldeaux, J., Dick and F., Pillichshammer. Duality theory and propagation rules for generalized nets. Submitted, 2009. (286)
[10] J., Beck. A two-dimensional van Aardenne Ehrenfest theorem in irregularities of distribution. Compos. Math., 72:269–339, 1989. (66)
[11] J., Beck and Chen, W. W. L.. Irregularities of distribution. Cambridge University Press, Cambridge, 1987. (61)
[12] R., Béjian. Minoration de la discrépance d'une suite quelconque sur T. Acta Arith., 41:185–202, 1982. (66)
[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)
[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)
[15] D., Bilyk and M. T., Lacey. On the small ball inequality in three dimensions. Duke Math. J., 143:81–115, 2008. (67)
[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)
[17] T., Blackmore and G. H., Norton. Matrix-product codes over Fq. Appl. Algebra Eng. Comm. Comput., 12:477–500, 2001. (288, 289)
[18] P., Bratley and B. L., Fox. Algorithm 659: Implementing Sobol's quasirandom sequence generator. ACM Trans. Math. Softw., 14:88–100, 1988. (267)
[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)
[20] H., Chaix and H., Faure. Discrépance et diaphonie en dimension un. Acta Arith., 63:103–141, 1993. (In French.) (180)
[21] W. W., L.|Chen. On irregularities of point distribution. Mathematika, 27:153–170, 1980. (66)
[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)
[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)
[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)
[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)
[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)
[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)
[29] H., Davenport. Note on irregularities of distribution. Mathematika, 3:131–135, 1956. (66, 509)
[30] P. J., Davis. Circulant matrices. John Wiley & Sons, New York, Chichester, Brisbane, 1979. (326)
[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)
[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)
[33] J., Dick. On the convergence rate of the component-by-component construction of good lattice rules. J. Complexity, 20:493–522, 2004. (390)
[34] J., Dick. The construction of extensible polynomial lattice rules with small weighted star discrepancy. Math. Comp., 76:2077–2085, 2007. (335)
[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)
[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)
[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)
[38] J., Dick. The decay of the walsh coefficients of smooth functions. Bull. Austral. Math. Soc., 80:430–453, 2009. (434, 463)
[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)
[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)
[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)
[42] J., Dick and P., Kritzer. Duality theory and propagation rules for generalized digital nets. Math. Comp., 79:993–1017, 2010. (473, 474)
[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)
[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)
[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)
[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)
[47] J., Dick and H., Niederreiter. On the exact t-value of Niederreiter and Sobol′ sequences. J. Complexity, 24:572–581, 2008. (265)
[48] J., Dick and H., Niederreiter. Duality for digital sequences. J. Complexity, 25:406–414, 2009. (244, 256)
[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)
[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)
[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)
[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)
[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)
[54] J., Dick, I. H., Sloan, X., Wang and H., Woźniakowski. Liberating the weights. J. Complexity, 20:593–623, 2004. (39, 368)
[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)
[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)
[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)
[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)
[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)
[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)
[61] M., Drmota and R. F., Tichy. Sequences, Discrepancies and Applications. Springer, Berlin, 1997. (xi, 46, 50, 60, 68, 90)
[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)
[63] Y., Edel and J., Bierbrauer. Families of ternary (t, m, s)-nets related to BCH-codes. Monatsh. Math., 132:99–103, 2001. (256)
[64] P., Erdős and P., Turán. On a problem in the theory of uniform distribution. I. Indagationes Math., 10:370–378, 1948. (68)
[65] P., Erdős and P., Turán. On a problem in the theory of uniform distribution. II. Indagationes Math., 10:406–413, 1948. (68)
[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)
[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)
[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)
[69] H., Faure. On the star-discrepancy of generalized Hammersley sequences in two dimensions. Monatsh. Math., 101:291–300, 1986. (83)
[70] H., Faure. Good permutations for extreme discrepancy. J. Number Theory, 42:47–56, 1992. (82)
[71] H., Faure. Discrepancy and diaphony of digital (0, 1)-sequences in prime base. Acta Arith., 117:125–148, 2005. (82, 180)
[72] H., Faure. Irregularities of distribution of digital (0, 1)-sequences in prime base. Integers, 5:A7, 12 pp. (electronic), 2005. (82, 180)
[73] H., Faure. Van der Corput sequences towards general (0, 1)-sequences in base b. J. Theor. Nombres Bordeaux, 19:125–140, 2007. (82)
[74] H., Faure. Star extreme discrepancy of generalized two-dimensional Hammersley point sets. Unif. Distrib. Theory, 3:45–65, 2008. (83, 180)
[75] H., Faure and H., Chaix. Minoration de discrepance en dimension deux. Acta Arith., 76:149–164, 1996. (In French.) (180)
[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)
[77] H., Faure and F., Pillichshammer. Lp discrepancy of generalized two-dimensional Hammersley point sets. Monatsh. Math., 158:31–61, 2009. (509)
[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)
[79] N. J., Fine. On the Walsh functions. Trans. Amer. Math. Soc., 65:372–414, 1949. (434, 436, 437, 446, 567)
[80] B. L., Fox. Algorithm 647: Implementation and relative efficiency of quasirandom sequence generators. ACM Trans. Math. Softw., 12:362–376, 1986. (267)
[81] B. L., Fox. Strategies for quasi-Monte Carlo. Kluwer Academic, Boston, MA, 1999. (1)
[82] K., Frank and S., Heinrich. Computing discrepancies of Smolyak quadrature rules. J. Complexity, 12:287–314, 1996. (32)
[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)
[84] K. K., Frolov. Upper bound of the discrepancy in metric Lp,2 ≤ p < ∞. Dokl. Akad. NaukSSSR, 252:805–807, 1980. (66, 509)
[85] P., Glasserman. Monte Carlo methods in financial engineering, vol. 53 of Applications of Mathematics (New York). Springer-Verlag, New York, 2004. (1,13)
[86] M., Gnewuch. Bracketing numbers for axis-parallel boxes and applications to geometric discrepancy. J. Complexity, 24:154–172, 2008. (90, 106)
[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)
[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)
[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)
[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)
[91] J., Hartinger and V., Ziegler. On corner avoidance properties of random-start Halton sequences. SIAM J. Numer. Anal., 45:1109–1121, 2007. (401)
[92] S., Heinrich. Efficient algorithms for computing the L2 discrepancy. Math. Comp., 65:1621–1633, 1996. (32)
[93] S., Heinrich. Some open problems concerning the star-discrepancy. J. Complexity, 19:416–419, 2003. (92)
[94] S., Heinrich, F. J., Hickernell and R. X., Yue. Optimal quadrature for Haar wavelet spaces. Math. Comp., 73:259–277, 2004. (431)
[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)
[96] P., Hellekalek. General discrepancy estimates: the Walsh function system. Acta Arith., 67:209–218, 1994. (68, 105)
[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)
[98] P., Hellekalek. Digital (t, m, s)-nets and the spectral test. Acta Arith., 105:197–204, 2002. (178, 179)
[99] P., Hellekalek and H., Leeb. Dyadic diaphony. Acta Arith., 80:187–196, 1997. (103, 104)
[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)
[101] F. J., Hickernell. Quadrature error bounds with applications to lattice rules. SIAM J. Numer. Anal., 33:1995–2016, 1996. (xi)
[102] F. J., Hickernell. A generalized discrepancy and quadrature error bound. Math. Comp., 67:299–322, 1998. (25)
[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)
[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)
[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)
[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)
[107] F. J., Hickernell and H., Niederreiter. The existence of good extensible rank-1 lattices. J. Complexity, 19:286–300, 2003. (217, 222, 330)
[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)
[109] A., Hinrichs. Covering numbers, Vapnik–Červonenkis classes and bounds for the star-discrepancy. J. Complexity, 20:477–483, 2004. (90)
[110] A., Hinrichs, F., Pillichshammer and W. Ch., Schmid. Tractability properties of the weighted star discrepancy. J. Complexity, 24:134–143, 2008. (99, 102)
[111] E., Hlawka. Funktionen von beschrankter Variation in der Theorie der Gleichverteilung. Ann. Mat. PuraAppl., 54:325–333, 1961. (In German.) (xi, 33)
[112] E., Hlawka. Über die Diskrepanz mehrdimensionaler Folgen mod 1. Math. Z., 77:273–284, 1961. (In German.) (18, 33)
[113] E., Hlawka. Zur angenäherten Berechnung mehrfacher Integrale. Monatsh. Math., 66:140–151, 1962. (In German.) (84)
[114] L. K., Hua and Y., Wang. Applications of number theory to numerical analysis. Springer, Berlin, 1981. (xi, 74)
[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)
[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)
[117] S., Joe and F. Y., Kuo. Constructing Sobol′ sequences with better two-dimensional projections. SIAM J. Sci. Comput., 30:2635–2654, 2008. (267)
[118] S., Joe and I. H., Sloan. On computing the lattice rule criterion R. Math. Comp., 59:557–568, 1992. (85)
[119] Y., Katznelson. An introduction to harmonic analysis. Cambridge Mathematical Library. Cambridge University Press, Cambridge, third edition, 2004. (566)
[120] A., Keller. Myths of computer graphics. In Monte Carlo and quasi-Monte Carlo methods 2004, pp. 217-243. Springer, Berlin, 2006. (1)
[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)
[122] J. F., Koksma. Some theorems on Diophantine inequalities. Scriptum no. 5, Math. Centrum Amsterdam, 1950. (68)
[123] N. M., Korobov. Approximate evaluation of repeated integrals. Dokl. Akad. Nauk SSSR, 124:1207–1210, 1959. (84)
[124] N. M., Korobov. Properties and calculation of optimal coefficients. Dokl. Akad. Nauk SSSR, 132:1009–1012, 1960. (In Russian.) (106, 306)
[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)
[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)
[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)
[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)
[129] P., Kritzer and F., Pillichshammer. Constructions of general polynomial lattices for multivariate integration. Bull. Austral. Math. Soc., 76:93–110, 2007. (384)
[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)
[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)
[132] G., Larcher. A best lower bound for good lattice points. Monatsh. Math., 104:45–51, 1987. (87)
[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)
[134] G., Larcher. Nets obtained from rational functions over finite fields. Acta Arith., 63:1–13, 1993. (180, 316)
[135] G., Larcher. On the distribution of an analog to classical Kronecker-sequences. J. Number Theory, 52:198–215, 1995. (134, 180)
[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)
[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)
[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)
[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)
[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)
[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)
[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)
[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)
[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)
[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)
[146] G., Larcher, F., Pillichshammer and K., Scheicher. Weighted discrepancy and high-dimensional numerical integration. BIT, 43:123–137, 2003. (180)
[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)
[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)
[149] K. M., Lawrence. A combinatorial characterization of (t, m, s)-nets in base b. J. Combin. Des., 4:275–293, 1996. (240, 242)
[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)
[151] P., L'Ecuyer. Quasi-Monte Carlo methods with applications in finance. Finance and Stochastics, 13:307–349, 2009. (1)
[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)
[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)
[154] Ch., Lemieux. Monte Carlo and quasi-Monte Carlo sampling. Springer Series in Statistics. Springer, New York, 2008. (1, 13, 401)
[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)
[156] G., Leobacher and F., Pillichshammer. Bounds for the weighted Lp discrepancy and tractability of integration. J. Complexity, 19:529–547, 2003. (107)
[157] R., Lidl and H., Niederreiter. Introduction to finite fields and their applications. Cambridge University Press, Cambridge, first edition, 1994. (254, 255, 299)
[158] W.-L., Loh. On the asymptotic distribution of scrambled net quadrature. Ann. Statist., 31:1282–1324, 2003. (412)
[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)
[160] J., Matoušek. On the L2-discrepancy for anchored boxes. J. Complexity, 14:527–556, 1998. (400, 555)
[161] J., Matoušek. Geometric discrepancy. Springer, Berlin, 1999. (400, 432)
[162] J., Matoušek and J., Nešetril. Invitation to discrete mathematics. Oxford University Press, Oxford, second edition, 2009. (238)
[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)
[164] G. L., Mullen. Orthogonal hypercubes and related designs. J. Statist. Plann. Inference, 73:177–188, 1998. (239)
[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)
[166] G. L., Mullen and G., Whittle. Point sets with uniformity properties and orthogonal hypercubes. Monatsh. Math., 113:265–273, 1992. (239)
[167] H., Niederreiter. On the distribution of pseudo-random numbers generated by the linear congruential method. III. Math. Comp., 30:571–597, 1976. (221)
[168] H., Niederreiter. Existence of good lattice points in the sense of Hlawka. Monatsh. Math., 86:203–219, 1978. (87, 180)
[169] H., Niederreiter. Low-discrepancy point sets. Monatsh. Math., 102:155–167, 1986. (245)
[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)
[171] H., Niederreiter. Quasi-Monte Carlo methods and pseudo-random numbers. Bull. Amer. Math. Soc., 84:957–1041, 1986. (xi)
[172] H., Niederreiter. Point sets and sequences with small discrepancy. Monatsh. Math., 104:273–337, 1987. (xi, 108, 117, 132, 153, 180, 234, 235)
[173] H., Niederreiter. Low-discrepancy and low-dispersion sequences. J. Number Theory, 30:51–70, 1988. (xi, xii, 263, 264, 268)
[174] H., Niederreiter. A combinatorial problem for vector spaces over finite fields. Discrete Math., 96:221–228, 1991. (246)
[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)
[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)
[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)
[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)
[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)
[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)
[181] H., Niederreiter. Error bounds for quasi-Monte Carlo integration with uniform point sets. J. Comput. Appl. Math., 150:283–292, 2003. (15)
[182] H., Niederreiter. The existence of good extensible polynomial lattice rules. Monatsh. Math., 139:295–307, 2003. (330, 331)
[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)
[184] H., Niederreiter. Constructions of (t, m, s)-nets and (t, i)-sequences. Finite Fields Appl., 11:578–600, 2005. (244, 253, 286, 347)
[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)
[186] H., Niederreiter and F., Özbudak. Constructions of digital nets using global function fields. Acta Arith., 105:279–302, 2002. (268)
[187] H., Niederreiter and F., Özbudak. Matrix-product constructions of digital nets. Finite Fields Appl., 10:464–479, 2004. (288, 289)
[188] H., Niederreiter and F., Pillichshammer. Construction algorithms for good extensible lattice rules. Constr. Approx., 30:361–393, 2009. (337)
[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)
[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)
[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)
[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)
[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)
[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)
[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)
[196] H., Niederreiter and C. P., Xing. Constructions of digital nets. Acta Arith., 102:189–197, 2002. (294)
[197] H., Niederreiter and C. P., Xing. Algebraic geometry in coding theory and cryptography. Princeton University Press, Princeton and Oxford, 2009. (268, 572)
[198] E., Novak. Numerische Verfahren fur hochdimensionale Probleme und der Fluch der Dimension. Jahresber. Deutsch. Math.-Verein., 101:151–177, 1999. (In German.) (89)
[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)
[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)
[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)
[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)
[203] D., Nuyens. Fast construction of good lattice rules. PhD thesis, Departement Computerwetenschappen, Katholieke Universiteit Leuven, 2007. (323)
[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)
[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)
[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)
[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)
[208] A. B., Owen. Scrambled net variance for integrals of smooth functions. Ann. Statist., 25:1541–1562, 1997. (396,424, 425)
[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)
[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)
[211] A. B., Owen. Local antithetic sampling with scrambled nets. Ann. Statist., 36:2319–2343, 2008. (401, 424, 425, 431)
[212] F., Pillichshammer. On the Lp -discrepancy of the Hammersley point set. Monatsh. Math., 136:67–79, 2002. (180)
[213] F., Pillichshammer. Improved upper bounds for the star discrepancy of digital nets in dimension 3. Acta Arith., 108:167–189, 2003. (180, 182)
[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)
[215] F., Pillichshammer and G., Pirsic. The quality parameter of cyclic nets and hyperplane nets. Unif. Distrib. Theory, 4:69–79, 2009. (352, 353)
[216] G., Pirsic. Schnell konvergierende Walshreihen über Gruppen. Master's thesis, Institute for Mathematics, University of Salzburg, (In German.) 1995. (559)
[217] G., Pirsic. Embedding theorems and numerical integration of Walsh series over groups. PhD thesis, Institute for Mathematics, University of Salzburg, 1997. (127, 446)
[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)
[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)
[220] G., Pirsic. A small taxonomy of integration node sets. Österreich. Akad. Wiss. Math.-Natur. Kl. Sitzungsber. II, 214:133-140 (2006), 2005. (349)
[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)
[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)
[223] P. D., Proĭnov. Symmetrization of the van der Corput generalized sequences. Proc. Jap. Acad. Ser. A Math. Sci., 64:159–162, 1988. (509)
[224] C. M., Rader. Discrete Fourier transforms when the number of data samples is prime. Proc. IEEE, 5:1107–1108, 1968. (325)
[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)
[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)
[227] M. Yu., Rosenbloom and M. A., Tsfasman. Codes in the m -metric. Problemi Peredachi Inf., 33:45–52, 1997. (245)
[228] K. F., Roth. On irregularities of distribution. Mathematika, 1:73–79, 1954. (xii, 60, 61, 82)
[229] K. F., Roth. On irregularities of distribution III. Acta Arith., 35:373–384, 1979. (66, 509)
[230] K. F., Roth. On irregularities of distribution IV. Acta Arith., 37:67–75, 1980. (66, 509)
[231] J., Sándor, D. S., Mitrinović and B., Crstici. Handbook of number theory. I.Springer, Dordrecht, 2006. Second printing of the 1996 original. (81)
[232] F., Schipp, W. R., Wade and P., Simon. Walsh series. An introduction to dyadic harmonic analysis. Adam Hilger Ltd., Bristol, 1990. (559, 567)
[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)
[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)
[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)
[236] W. Ch., Schmid and R., Wolf. Bounds for digital nets and sequences. Acta Arith., 78:377–399, 1997. (155)
[237] W. M., Schmidt. Irregularities of distribution VII. Acta Arith., 21:45–50, 1972. (66)
[238] W. M., Schmidt. Irregularities of distribution. X. In Number theory and algebra, pp. 311-329. Academic Press, New York, 1977. (66)
[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)
[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)
[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)
[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)
[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)
[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)
[245] I. H., Sloan and S., Joe. Lattice methods for multiple integration. Oxford University Press, New York and Oxford, 1994. (88, 298)
[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)
[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)
[248] I. H., Sloan and A. V., Reztsov. Component-by-component construction of good lattice rules. Math. Comp., 71:263–273, 2002. (85)
[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)
[250] I. H., Sloan and H., Woźniakowski. Tractability of multivariate integration for weighted Korobov classes. J. Complexity, 17:697–721, 2001. (44)
[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)
[252] I. M., Sobol′. Functions of many variables with rapidly convergent Haar series. Soviet Math. Dokl., 1:655–658, 1960. (xiii)
[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)
[254] H., Stichtenoth. Algebraic function fields and codes. Universitext. Springer, Berlin, 1993. (572, 577, 580, 581)
[255] S., Tezuka. Polynomial arithmetic analogue of Halton sequences. ACM Trans. Model. Comput. Simul., 3:99–107, 1993. (266)
[256] S., Tezuka. Uniform random numbers: theory and practice. Kluwer International Series in Engineering and Computer Science. Kluwer, Boston, 1995. (1, 266)
[257] S., Tezuka and H., Faure. I -binomial scrambling of digital nets and sequences. J. Complexity, 19:744–757, 2003. (400)
[258] H., Triebel. Bases in function spaces, sampling, discrepancy, numerical integration. To appear, 2009. (34)
[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)
[260] J. L., Walsh. A closed set of normal orthogonal functions. Amer. J. Math., 45:5–24, 1923. (559, 567)
[261] X., Wang. A constructive approach to strong tractability using quasi-Monte Carlo algorithms. J. Complexity, 18:683–701, 2002. (223)
[262] X., Wang. Strong tractability of multivariate integration using quasi-Monte Carlo algorithms. Math. Comp., 72:823–838, 2003. (223)
[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)
[264] E., Weiss. Algebraic number theory. McGraw-Hill Book Co., Inc., New York, 1963. (572, 577)
[265] H., Weyl. Über die Gleichverteilung von Zahlen mod. Eins. Math. Ann., 77:313–352, 1916. (In German.) (xi, 47)
[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)
[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)
[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)
[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)
[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)
[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)
[272] S. K., Zaremba. Some applications of multidimensional integration by parts. Ann. Poln. Math., 21:85–96, 1968. (18, 33)
[273] A., Zygmund. Trigonometric series. Cambridge University Press, Cambridge, 1959. (434)
