A tight lower bound on the minimal dispersion
Numerical Analysis
2024-03-21 v3 Numerical Analysis
Abstract
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 class of test boxes, which allows us to reduce bounding the dispersion to a problem in extremal set theory. Specifically, we translate a lower bound on the size of -cover-free families to a lower bound on the inverse of the minimal dispersion of a point set. The lower bound we obtain matches the recently obtained upper bound on the minimal dispersion up to logarithmic terms.
Cite
@article{arxiv.2311.10666,
title = {A tight lower bound on the minimal dispersion},
author = {Matěj Trödler and Jan Volec and Jan Vybíral},
journal= {arXiv preprint arXiv:2311.10666},
year = {2024}
}