We give a new lower bound for the minimal dispersion of a point set in the unit cube and its
inverse function in the high dimension regime. This is done by considering only a very small …

In this note we present a construction which improves the best known bound on the minimal
dispersion of large volume boxes in the unit cube. Let d> 1. The dispersion of T⊂[0, 1] d is …

We improve some upper bounds for minimal dispersion on the cube and torus. Our new
ingredient is an improvement of a probabilistic lemma used to obtain upper bounds for …

A set of points with finite density is constructed in $\mathbb {R}^ d $, with $ d\geq2 $, by
adding points to a Poisson process such that any line segment of length $ O\left …

We prove upper and lower bounds on the minimal spherical dispersion, improving upon
previous estimates obtained by Rote and Tichy in (Anz Österreich Akad Wiss Math Nat Kl …