English

The Sobol' sequence is not quasi-uniform in dimension 2

Numerical Analysis 2024-01-24 v2 Numerical Analysis

Abstract

Are common quasi-Monte Carlo sequences quasi-uniform? While this question remains widely open, in this short note, we prove that the two-dimensional Sobol' sequence is not quasi-uniform. This result partially answers an unsolved problem of Sobol' and Shukhman (2007) in a negative manner.

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Cite

@article{arxiv.2311.05830,
  title  = {The Sobol' sequence is not quasi-uniform in dimension 2},
  author = {Takashi Goda},
  journal= {arXiv preprint arXiv:2311.05830},
  year   = {2024}
}

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5 pages