Work

Constructing optimal star discrepancy sets

Year: 2025

Type: article

Abstract: We provide in this paper a constructive proof of optimal L ∞ L_{\infty } star discrepancy values in dimension 2 for up to 21 points and up to 8 points in dimension 3. This extends work by White (Numer. Math. 27 (1976/77), no. 2, 157–164) for up to six points in dimension 2 and of Larcher and Pillichshammer (J. Comput. Appl. Math. 206 (2007), no. 2, 977–985) for two points in arbitrary dimensions. We show that these optimal sets have a far lower discrepancy than the previous references and, perhaps more importantly, present a very different structure.

Source: Proceedings of the American Mathematical Society Series B

DOI: 10.1090/bproc/254

Authors: François Clément, Carola Doerr, Kathrin Klamroth, Luís Paquete

Institutions: Centre National de la Recherche Scientifique, Sorbonne Université, LIP6, University of Wuppertal, University of Coimbra

Language: English

Topic: Mathematical Approximation and Integration

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $750