  Classical jittered sampling partitions $[0,1]^d$ into $m^d$ cubes for a
positive integer $m$ and randomly places a point inside each of them, providing
a point set of size $N=m^d$ with small discrepancy. The aim of this note is to
provide a construction of partitions that works for arbitrary $N$ and improves
straight-forward constructions. We show how to construct equivolume partitions
of the $d$-dimensional unit cube with hyperplanes that are orthogonal to the
main diagonal of the cube. We investigate the discrepancy of such point sets
and optimise the expected discrepancy numerically by relaxing the equivolume
constraint using different black-box optimisation techniques.
