Work

Disproving the quasi-uniformity of the Halton sequences and of some Halton-type sequences

Year: 2026

Type: article

Abstract: In this short article, we prove that the Halton sequence, one of the most well-known low-discrepancy sequences, is not quasi-uniform in any dimension d ≥ 2 with any pairwise relatively prime bases. We further disprove the quasi-uniformity of some Halton-type sequences, including the p -dimensional Faure sequence in base p , p ∈ P , which provides an alternative proof of the known results.

Source: Journal of Complexity

DOI: 10.1016/j.jco.2026.102047

Authors: Takashi Goda, Roswitha Hofer, Kosuke Suzuki

Institutions: The University of Tokyo, Johannes Kepler University of Linz, Yamagata University

Language: English

Topic: Mathematical Approximation and Integration

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,680

Funder: Japan Society for the Promotion of Science