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Digital almost nets
Preprint
25 February 2021
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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.