Hammersley Point Sets and Inverse of Star-Discrepancy

Christian Weiß

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arXiv · 2411.10363

Hammersley Point Sets and Inverse of Star-Discrepancy

Christian Weiß

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Abstract

We establish the existence of $N$-point sets in dimension $d$ whose star-discrepancy is bounded above by $2.4631832 \sqrt{\frac{d}{N}}$, where the numerical constant improves upon all previously known bounds. This improvement is obtained by combining a recent result by Gnewuch on bracketing numbers in high dimensions with discrepancy bounds for Hammersley point sets due to Atanassov in dimensions $1 \leq d \leq 4$.

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Christian Weiß. 2024-11-15. Hammersley Point Sets and Inverse of Star-Discrepancy. https://arxiv.org/abs/2411.10363

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