Year: 2025
Type: article
Abstract: We investigate $$L_2$$ 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 $$L_2$$ 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 $$L_2$$ L 2 -discrepancy of weak Latin hypercubes. We determine asymptotically tight bounds for $$d \ge 3$$ d ≥ 3 and even the precise (dimension dependent) constant in front of the dominating term for $$d \ge 4$$ d ≥ 4 .
Source: Monatshefte für Mathematik
Author: Nicolas Nagel
Institution: Chemnitz University of Technology
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
Award: G6754681371
OpenAlex ID: W4409786415