# Incremental space-filling design based on coverings and spacings: improving upon low discrepancy sequences

arXiv: https://arxiv.org/abs/2106.05833 · HTML: https://mlsanity.com/paper/2106.05833/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Jun 2021.

## Built on by (most cited first, 2 of 2)

- [Quasi-uniform designs with optimal and near-optimal uniformity constant](https://mlsanity.com/paper/2112.10401/) (2021)
- [Non-asymptotic quantisation of spherically symmetric distributions](https://mlsanity.com/paper/2605.12568/) (2026)

## Abstract (arXiv)

The paper addresses the problem of defining families of ordered sequences xii∈ N of elements of a compact subset X of Rd whose prefixes Xn=xii=1n, for all orders n, have good space-filling properties as measured by the dispersion (covering radius) criterion. Our ultimate aim is the definition of incremental algorithms that generate sequences Xn with small optimality gap, i.e., with a small increase in the maximum distance between points of X and the elements of Xn with respect to the optimal solution Xn^star. The paper is a first step in this direction, presenting incremental design algorithms with proven optimality bound for one-parameter families of criteria based on coverings and spacings that both converge to dispersion for large values of their parameter. The examples presented show that the covering-based method outperforms state-of-the-art competitors, including coffee-house, suggesting that it inherits from its guaranteed 50% optimality gap.