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On the $L_2$-discrepancy of Latin hypercubes
On the $L_2$-discrepancy of Latin hypercubes
- Publication Year :
- 2025
-
Abstract
- 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 $d \geq 4$.<br />Comment: To appear in Monatshefte f\"ur Mathematik
- Subjects :
- Mathematics - Numerical Analysis
Mathematics - Combinatorics
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2502.20828
- Document Type :
- Working Paper