On the Expected ℒ₂–Discrepancy of Jittered Sampling

Abstract For m, d ∈ ℕ, a jittered sample of N = m points can be constructed by partitioning [0, 1] into axis-aligned equivolume boxes and placing one point independently uniformly at random inside each box. We utilise formula for the expected ℒ 2 −discrepancy stratified samples stemming from general partitions which recently appeared, to derive closed form expression set any ℕ. As second main result we similar Hickernell also takes all projections lower dimensional faces unit cube account.