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

2014/12/30 by Mordechay B. Levin, Levin, Mordechay B.
Mathematics · #11K38 #Analytic Number Theory Research #FOS: Mathematics #Mathematical Approximation and Integration #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1412.8705

openalex publication_date 2014/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 → ∞} N ln^-s(N) D_N gt;0.

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