A good permutation for one-dimensional diaphony

Florian Pausinger*, Wolfgang Ch Schmid

*Corresponding author for this work

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

In this article we focus on two aspects of one-dimensional diaphony F(S σ b, N) of generalised van der Corput sequences in arbitrary bases. First we give a permutation with the best distribution behaviour concerning the diaphony known so far. We improve a result of Chaix and Faure from 1993 from a value of 1.31574... for a permutation in base 19 to 1.13794... for our permutation in base 57. Moreover for an infinite sequence X and its symmetric version X̃, we analyse the connection between the diaphony F(X, N) and the L 2-discrepancy L 2(X̃, N) using another result of Chaix and Faure. Therefore we state an idea how to get a lower bound for the diaphony of generalised van der Corput sequences in arbitrary base b.

Original languageEnglish
Pages (from-to)307-322
Number of pages16
JournalMonte Carlo Methods and Applications
Volume16
Issue number3-4
DOIs
Publication statusPublished - Dec 2010
Externally publishedYes

Keywords

  • Diaphony
  • Generalised van der Corput sequence

ASJC Scopus subject areas

  • Statistics and Probability
  • Applied Mathematics

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