The motivation for introducing and studying the concept of (t, m, s)-nets and (T, s)- sequences was to generate point sets (also sometimes in high dimensions) with as small a discrepancy as possible. In this chapter we give an overview of theoretical results for the discrepancy of (digital) nets and sequences.
While singular results were already given by Sobol′  and by Faure , the first systematic study of the discrepancy of nets was given by Niederreiter . These results can also be found in [177, Chapter 4]. Further results on the star discrepancy of digital nets and sequences, mainly for low dimensions, can be found in [40, 71, 72, 74, 125, 126, 144, 145, 213].
After the work of Niederreiter [172, 177], metrical and average results on the discrepancy of nets and net-sequences were given; see, for instance, [134, 135, 136, 138, 140]. Further, the study of weighted discrepancy of net-type point sets also received considerable attention in recent years (see, for example, [49, 146]).
Even though we have many results for the extreme and star discrepancies, very little is known about concrete theoretical estimates for the Lp-discrepancy, especially for net-type point sets. Singular results in this direction can be found in [20, 22, 75, 142, 143, 212, 244] (results concerning the L2-discrepancy are presented in Chapter 16).