New bounds on the minimal dispersion
Abstract
We provide a new construction for a set of boxes approximating axis-parallel boxes of fixed volume in [0, 1]d. This improves upper bounds for the minimal dispersion of a point set in the unit cube and its inverse in both the periodic and non-periodic settings in certain regimes. Up to double logarithmic factor, our bounds are sharp. We also apply our construction to k-dispersion.
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