On a partition with a lower expected ${\mathcal{L}}_2$-discrepancy than classical jittered sampling

Abstract

We prove that classical jittered sampling of the $d$-dimensional unit cube does not yield the smallest expected ${\mathcal{L}}_2$-discrepancy among all stratified samples with $N=m^d$ points. Our counterexample can be given explicitly and consists of convex partitioning sets of equal volume.

arXiv comment12 pages; revised version contains results of numerical experiments

References in corpus (3)

• A Lower Bound for the Discrepancy of a Random Point Set
• A Sharp Discrepancy Bound for Jittered Sampling
• A Generalized Faulhaber Inequality, Improved Bracketing Covers, and Applications to Discrepancy

Cited by in corpus (1)

• Expected uniform integration approximation under general equal measure partition