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.
 Publication:

arXiv eprints
 Pub Date:
 June 2021
 arXiv:
 arXiv:2106.01937
 Bibcode:
 2021arXiv210601937K
 Keywords:

 Mathematics  Number Theory;
 11K38;
 60C05 (primary);
 and 05A18;
 60D99 (secondary)
 EPrint:
 12 pages