On the Discrepancy of Two Families of Permuted Van der Corput Sequences

Florian Pausinger, Alev Topuzoglu

Research output: Contribution to journalArticlepeer-review

152 Downloads (Pure)

Abstract

A permuted van der Corput sequence Sσ b in base b is a one-dimensional, infinite sequence of real numbers in the interval [0, 1), generation of which involves a permutation σ of the set {0, 1,...,b − 1}. These sequences are known to have low discrepancy DN , i.e. t(Sσ b ) := lim supN→∞ DN (Sσ b )/ log N is finite. Restricting to prime bases p we present two families of generating permutations. We describe their elements as polynomials over finite fields Fp in an explicit way. We use this characterization to obtain bounds for t(Sσ p ) for permutations σ in these families. We determine the best permutations in our first family and show that all permutations of the second family improve the distribution behavior of classical van der Corput sequences in the sense that t(Sσ p ) < t(Sid p ).
Original languageEnglish
Pages (from-to)47-64
Number of pages18
JournalUniform Distribution Theory
Volume13
Issue number1
DOIs
Publication statusPublished - 01 Jun 2018

Keywords

  • van der Corput Sequence
  • Discrepancy
  • Permutation

Fingerprint Dive into the research topics of 'On the Discrepancy of Two Families of Permuted Van der Corput Sequences'. Together they form a unique fingerprint.

Cite this