Digital almost nets

02/25/2021

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by   Boris Bukh, et al.

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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.