On the star discrepancy of sequences in the unit interval

2014/07/08 by Gerhard Larcher, Larcher, Gerhard
Computer Science · Mathematics · #11K38 #Analytic Number Theory Research #Digital Image Processing Techniques #FOS: Mathematics #Mathematical Approximation and Integration #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1407.2094

openalex publication_date 2014/07/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is known that there is a constant c > 0 such that for every sequence x₁, x₂, … in [0,1) we have for the star discrepancy D_N^* of the first N elements of the sequence that N D_N^* ≥ c ⋅ log N holds for infinitely many N. Let c^* be the supremum of all such c with this property. We show c^* > 0.0646363, thereby improving the until now known estimates.

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