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

作者：Takashi Goda · 发表于：Proceedings of the American Mathematical Society · 年份：2024 · DOI：10.1090/proc/16816 · 被引用次数：6 · 研究领域：Mathematical Approximation and Integration、Cryptography and Residue Arithmetic、Analytic Number Theory Research

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 [Math. Comput. Simulation 75 (2007), pp. 80–86] in a negative manner.