# An Upper Bound of the Minimal Dispersion via Delta Covers

arXiv: https://arxiv.org/abs/1701.06430 · HTML: https://mlsanity.com/paper/1701.06430/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Jan 2017.

## Built on by (most cited first, 1 of 1)

- [Frustratingly Easy Regularization on Representation Can Boost Deep Reinforcement Learning](https://mlsanity.com/paper/2205.14557/) (2022)

## Abstract (arXiv)

For a point set of n elements in the d-dimensional unit cube and a class of test sets we are interested in the largest volume of a test set which does not contain any point. For all natural numbers n, d and under the assumption of a delta-cover with cardinality vert Gammaδ vert we prove that there is a point set, such that the largest volume of such a test set without any point is bounded by fraclog vert Gammaδ vertn + δ. For axis-parallel boxes on the unit cube this leads to a volume of at most frac4dnlog(frac9nd) and on the torus to frac4dnlog (2n).