A lower bound for the dispersion on the torus

Mario Ullrich

doi:10.1016/j.matcom.2015.12.005

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arXiv · 1510.04617

A lower bound for the dispersion on the torus

Mario Ullrich

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Abstract

We consider the volume of the largest axis-parallel box in the $d$-dimensional torus that contains no point of a given point set $\mathcal{P}_n$ with $n$ elements. We prove that, for all natural numbers $d, n$ and every point set $\mathcal{P}_n$, this volume is bounded from below by $\min\{1,d/n\}$. This implies the same lower bound for the discrepancy on the torus.

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Mario Ullrich. 2015-10-15. A lower bound for the dispersion on the torus. https://doi.org/10.1016/j.matcom.2015.12.005

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