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

Published 10 Nov 2023 in math.NA and cs.NA | (2311.05830v2)

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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