On the lower bound of the discrepancy of Halton’s sequence II

Mordechay B. Levin

doi:10.1007/s40879-016-0103-7

On the lower bound of the discrepancy of Halton’s sequence II

Mordechay B. Levin

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

Let (Hs(n))n⩾1 be an s-dimensional generalized Halton’s sequence. Let DN∗ be the discrepancy of the sequence (Hs(n))n=1N. It is known that [InlineEquation not available: see fulltext.] as N→ ∞. In this paper, we prove that this estimate is exact. Namely, there exists a constant C(H_s) > 0 such thats [Equation not available: see fulltext.]

Original language	English
Pages (from-to)	874-885
Number of pages	12
Journal	European Journal of Mathematics
Volume	2
Issue number	3
DOIs	https://doi.org/10.1007/s40879-016-0103-7
State	Published - 1 Sep 2016

Bibliographical note

Publisher Copyright:
© 2016, Springer International Publishing AG.

Keywords

Ergodic adding machine
Halton’s sequence

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10.1007/s40879-016-0103-7

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abstract = "Let (Hs(n))n⩾1 be an s-dimensional generalized Halton{\textquoteright}s sequence. Let DN∗ be the discrepancy of the sequence (Hs(n))n=1N. It is known that [InlineEquation not available: see fulltext.] as N→ ∞. In this paper, we prove that this estimate is exact. Namely, there exists a constant C(Hs) > 0 such thats [Equation not available: see fulltext.]",

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AB - Let (Hs(n))n⩾1 be an s-dimensional generalized Halton’s sequence. Let DN∗ be the discrepancy of the sequence (Hs(n))n=1N. It is known that [InlineEquation not available: see fulltext.] as N→ ∞. In this paper, we prove that this estimate is exact. Namely, there exists a constant C(Hs) > 0 such thats [Equation not available: see fulltext.]

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KW - Halton’s sequence

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On the lower bound of the discrepancy of Halton’s sequence II

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