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On the $L_2$-discrepancy of Latin hypercubes

On the $L_2$-discrepancy of Latin hypercubes

Authors :
Nagel, Nicolas
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

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.2502.20828
Document Type :
Working Paper