A lower bound for the dispersion on the torus

Mario Ullrich

Mathematics and Computers in Simulation (MATCOM), 2018, vol. 143, issue C, 186-190

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 Pn with n elements. We prove that, for all natural numbers d,n and every point set Pn, this volume is bounded from below by min{1,d/n}. This implies the same lower bound for the discrepancy on the torus.

Keywords: Dispersion; Discrepancy; Torus (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:143:y:2018:i:c:p:186-190

DOI: 10.1016/j.matcom.2015.12.005

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