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arXiv · 1810.11345

Improving a Constant in High-Dimensional Discrepancy Estimates

Hendrik Pasing·Christian Weiß
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Abstract

For all $s \geq 1$ and $N \geq 1$ there exist sequences $(z_1,\ldots,z_N)$ in $[0,1]^s$ such that the star-discrepancy of these points can be bounded by $$D_N^*(z_1,\ldots,z_N) \leq c \frac{\sqrt{s}}{\sqrt{N}}.$$ The best known value for the constant is $c=10$ as has been calculated by Aistleitner in \cite{Ais11}. In this paper we improve the bound to $c=9$.

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Hendrik Pasing, Christian Weiß. 2018-10-26. Improving a Constant in High-Dimensional Discrepancy Estimates. https://arxiv.org/abs/1810.11345

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