# The Partition Principle Revisited: Non-Equal Volume Designs Achieve Minimal Expected Star Discrepancy

arXiv: https://arxiv.org/abs/2603.00202 · HTML: https://mlsanity.com/paper/2603.00202/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 6 references that are in the map.
- First posted on arXiv 27 Feb 2026.

## Builds on (most cited first, 1 of 1)

- [A Sharp Discrepancy Bound for Jittered Sampling](https://mlsanity.com/paper/2103.15712/) (2021)

## Abstract (arXiv)

We study the expected star discrepancy under a newly designed class of non-equal volume partitions. The main contributions are twofold. First, we establish a strong partition principle for the star discrepancy, showing that our newly designed non-equal volume partitions yield stratified sampling point sets with lower expected star discrepancy than classical jittered sampling. Specifically, we prove that mathbbE(D*N(Z)) < mathbbE(D*N(Y)), where Y and Z represent jittered sampling and our non-equal volume partition sampling, respectively. Second, we derive explicit upper bounds for the expected star discrepancy under our non-equal volume partition models, which improve upon existing bounds for jittered sampling. Our results provide a theoretical foundation for using non-equal volume partitions in high-dimensional numerical integration.