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. In the case of random choice of points our bounds are sharp up to double logarithmic factor. We also apply our construction to k-dispersion. (c) 2022 Elsevier Inc. All rights reserved.
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