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arXiv · 2102.12872

Digital almost nets

Boris Bukh·Ting-Wei Chao
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Abstract

Digital nets (in base $2$) are the subsets of $[0,1]^d$ that contain the expected number of points in every not-too-small dyadic box. We construct sets that contain almost the expected number of points in every such box, but which are exponentially smaller than the digital nets. We also establish a lower bound on the size of such almost nets.

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Boris Bukh, Ting-Wei Chao. 2022-09-27. Digital almost nets. https://arxiv.org/abs/2102.12872

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