Hammersley Point Sets and Inverse of Star-Discrepancy
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911357131030528 |
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| author | Weiß, Christian |
| author_facet | Weiß, Christian |
| contents | 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 $1 \leq d \leq 4$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_10363 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hammersley Point Sets and Inverse of Star-Discrepancy Weiß, Christian Number Theory Numerical Analysis 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 $1 \leq d \leq 4$. |
| title | Hammersley Point Sets and Inverse of Star-Discrepancy |
| topic | Number Theory Numerical Analysis |
| url | https://arxiv.org/abs/2411.10363 |