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arXiv · 2511.21153

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

Takashi Goda·Roswitha Hofer·Kosuke Suzuki
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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 $d \ge 2$ 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 $p$, $p \in \mathbb{P}$, which provides an alternative proof of the known results.

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Takashi Goda, Roswitha Hofer, Kosuke Suzuki. 2026-03-05. Disproving the quasi-uniformity of the Halton sequences and of some Halton-type sequences. https://arxiv.org/abs/2511.21153

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