New bounds on the density of lattice coverings
Number Theory
2020-06-03 v1 Information Theory
math.IT
Metric Geometry
Abstract
We obtain new upper bounds on the minimal density of lattice coverings of Euclidean space by dilates of a convex body K. We also obtain bounds on the probability (with respect to the natural Haar-Siegel measure on the space of lattices) that a randomly chosen lattice L satisfies that L+K is all of space. As a step in the proof, we utilize and strengthen results on the discrete Kakeya problem.
Cite
@article{arxiv.2006.00340,
title = {New bounds on the density of lattice coverings},
author = {Or Ordentlich and Oded Regev and Barak Weiss},
journal= {arXiv preprint arXiv:2006.00340},
year = {2020}
}