Disproving the quasi-uniformity of the Halton sequences and of some Halton-type sequences
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866918371982835712 |
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| author | Goda, Takashi Hofer, Roswitha Suzuki, Kosuke |
| author_facet | Goda, Takashi Hofer, Roswitha Suzuki, Kosuke |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_21153 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Disproving the quasi-uniformity of the Halton sequences and of some Halton-type sequences Goda, Takashi Hofer, Roswitha Suzuki, Kosuke Number Theory 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. |
| title | Disproving the quasi-uniformity of the Halton sequences and of some Halton-type sequences |
| topic | Number Theory |
| url | https://arxiv.org/abs/2511.21153 |