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

Mordechay B. Levin

doi:10.1016/j.crma.2016.02.003

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

Mordechay B. Levin

Department of Mathematics

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

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Abstract

Let (H_s(n))_n≥1 be an s-dimensional Halton's sequence. Let D_N be the discrepancy of the sequence (H_s(n))_n=1^N. It is known that ND_N=O(ln^s N) as N→∞. In this paper, we prove that this estimate is exact:lim_N→∞Nln^-s (N)D_N>0.

Original language	English
Pages (from-to)	445-448
Number of pages	4
Journal	Comptes Rendus Mathematique
Volume	354
Issue number	5
DOIs	https://doi.org/10.1016/j.crma.2016.02.003
State	Published - 1 May 2016

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© 2016 Académie des sciences.

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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.",

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N2 - 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.

AB - 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.

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

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