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.

17 pages; final version uploaded