Point sets and sequences with small discrepancy

A systematic theory of a class of point sets called (t, m, s)-nets and of a class of sequences called (t, s)-sequences is developed. On the basis of this theory, point sets and sequences in thes-dimensional unit cube with the smallest discrepancy that is currently known are constructed. Various connections with other areas arise in this work, e.g. with orthogonal latin squares, finite projective planes, finite fields, and algebraic coding theory. Applications of the theory of (t, m, s)-nets to two methods for pseudorandom number generation, namely the digital multistep method and the GFSR method, are presented. Several open problems, mostly of a combinatorial nature, are stated.The author wants to thank the Universität Hannover (West Germany) for its hospitality during the period when most of this research was carried out. The results of this paper were presented at the Colloquium on Irregularities of Partitions at Fertöd (Hungary), July 7–11, 1986.