On the $L_2$-discrepancy of Latin hypercubes
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912251755102208 |
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| author | Nagel, Nicolas |
| author_facet | Nagel, Nicolas |
| contents | We investigate $L_2$-discrepancies of what we call weak Latin hypercubes. In this case it turns out that there is a precise equivalence between the extreme and periodic $L_2$-discrepancy which follows from a much broader result about generalized energies for weighted point sets.
Motivated by this we study the asymptotics of the optimal $L_2$-discrepancy of weak Latin hypercubes. We determine asymptotically tight bounds for $d \geq 3$ and even the precise (dimension dependent) constant in front of the dominating term for $d \geq 4$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_20828 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the $L_2$-discrepancy of Latin hypercubes Nagel, Nicolas Numerical Analysis Combinatorics We investigate $L_2$-discrepancies of what we call weak Latin hypercubes. In this case it turns out that there is a precise equivalence between the extreme and periodic $L_2$-discrepancy which follows from a much broader result about generalized energies for weighted point sets. Motivated by this we study the asymptotics of the optimal $L_2$-discrepancy of weak Latin hypercubes. We determine asymptotically tight bounds for $d \geq 3$ and even the precise (dimension dependent) constant in front of the dominating term for $d \geq 4$. |
| title | On the $L_2$-discrepancy of Latin hypercubes |
| topic | Numerical Analysis Combinatorics |
| url | https://arxiv.org/abs/2502.20828 |