On the lower bound of the discrepancy of Halton's sequence I

Mordechay B. Levin

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3 Scopus citations

Abstract

Let (Hs(n))n≥1 be an s-dimensional Halton's sequence. Let DN be the discrepancy of the sequence (Hs(n))n=1N. It is known that NDN=O(lns N) as N→∞. In this paper, we prove that this estimate is exact:limN→∞Nln-s (N)DN>0.

Original languageEnglish
Pages (from-to)445-448
Number of pages4
JournalComptes Rendus Mathematique
Volume354
Issue number5
DOIs
StatePublished - 1 May 2016

Bibliographical note

Publisher Copyright:
© 2016 Académie des sciences.

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