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.
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