English

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 dd-dimensional unit cube does not yield the smallest expected L2\mathcal{L}_2-discrepancy among all stratified samples with N=mdN=m^d 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

R2 v1 2026-06-24T02:48:07.475Z