# A note on minimal dispersion of point sets in the unit cube

@article{Sosnovec2017ANO,
title={A note on minimal dispersion of point sets in the unit cube},
author={Jakub Sosnovec},
journal={Eur. J. Comb.},
year={2017},
volume={69},
pages={255-259}
}
25 Citations
• Mathematics
ArXiv
• 2020
We show that, for every set of $n$ points in the $d$-dimensional unit cube, there is an empty axis-parallel box of volume at least $\Omega(d/n)$ as $n\to\infty$ and $d$ is fixed. In the opposite
It is proved that there is a point set, such that the largest volume of such a test set without any point is bounded above by $$\frac {\log \vert \varGamma _\delta \vert }{n} + \delta}$$.
Discrepancy theory is a classical well established area of research in geometry and numerical integration (see [2], [8], [15], [17]). Recently, in [18], a new phenomenon has been discovered. A
• Mathematics
IWOCA
• 2021
This work requires that a single point set P simultaneously pierces each translate of each shape from some family F, and denotes the lowest possible density of such an F-piercing point set by πT (F).

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It is proved that there is a point set, such that the largest volume of such a test set without any point is bounded above by $$\frac {\log \vert \varGamma _\delta \vert }{n} + \delta}$$.
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