An improved bound for the star discrepancy of sequences in the unit\n interval

2015/11/12 by Gerhard Larcher, Larcher, Gerhard, Florian Puchhammer +1
Mathematics · #11K06 #11K38 #Analytic Number Theory Research #FOS: Mathematics #Mathematical Approximation and Integration #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1511.03869

openalex publication_date 2015/11/12 · 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,\nx₂,\… in [0,1) we have for the star discrepancy D^*_N of the first\nN elements of the sequence that N D^*_N\≥ c\⋅ \log N holds for\ninfinitely many N. Let c^* be the supremum of all such c with this\nproperty. We show c^*>0.065664679\…, thereby slightly improving the\nestimates known until now.\n

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