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arXiv · 1511.03869

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

Gerhard Larcher·Florian Puchhammer
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Abstract

It is known that there is a constant $c>0$ such that for every sequence $x_1, x_2,\ldots$ in $[0,1)$ we have for the star discrepancy $D^{*}_N$ of the first $N$ elements of the sequence that $N D^{*}_N\geq c\cdot \log N$ holds for infinitely many $N$. Let $c^{*}$ be the supremum of all such $c$ with this property. We show $c^{*}>0.065664679\ldots$, thereby slightly improving the estimates known until now.

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Gerhard Larcher, Florian Puchhammer. 2015-11-12. An improved bound for the star discrepancy of sequences in the unit interval. https://arxiv.org/abs/1511.03869

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