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The Algebraic-Geometry Approach to Low-Discrepancy Sequences

  • Harald Niederreiter
  • Chaoping Xing
Part of the Lecture Notes in Statistics book series (LNS, volume 127)

Abstract

We give a survey of recent work of the authors in which low-discrepancy sequences are constructed by new methods based on algebraic geometry. The most powerful of these methods employ algebraic curves over finite fields with many rational points. These methods yield significant improvements on all earlier constructions. In fact, we obtain (t, s)sequences in an arbitrary base b where for fixed b the quality parameter t has the least possible order of magnitude when considered as a function of the dimension s., namely t grows linearly in s.

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Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • Harald Niederreiter
    • 1
  • Chaoping Xing
    • 2
  1. 1.Institute of Information ProcessingAustrian Academy of SciencesViennaAustria
  2. 2.Department of MathematicsUniversity of Science and Technology of ChinaHefeiP.R. China

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