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.

12 pages; revised version contains results of numerical experiments

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