On a partition with a lower expected $\mathcal{L}_2$-discrepancy than classical jittered sampling
Number Theory
2021-10-20 v2
Abstract
We prove that classical jittered sampling of the -dimensional unit cube does not yield the smallest expected -discrepancy among all stratified samples with points. Our counterexample can be given explicitly and consists of convex partitioning sets of equal volume.
Cite
@article{arxiv.2106.01937,
title = {On a partition with a lower expected $\mathcal{L}_2$-discrepancy than classical jittered sampling},
author = {Markus Kiderlen and Florian Pausinger},
journal= {arXiv preprint arXiv:2106.01937},
year = {2021}
}
Comments
12 pages; revised version contains results of numerical experiments