Monatshefte für Mathematik

, Volume 104, Issue 4, pp 273–337

Point sets and sequences with small discrepancy

  • Harald Niederreiter

DOI: 10.1007/BF01294651

Cite this article as:
Niederreiter, H. Monatshefte für Mathematik (1987) 104: 273. doi:10.1007/BF01294651


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.

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • Harald Niederreiter
    • 1
  1. 1.Kommission für MathematikÖsterreichische Akademie der WissenschaftenWienAustria