# Quasi-uniform designs with optimal and near-optimal uniformity constant

arXiv: https://arxiv.org/abs/2112.10401 · HTML: https://mlsanity.com/paper/2112.10401/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 26 references that are in the map.
- First posted on arXiv 20 Dec 2021.

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

- [Incremental space-filling design based on coverings and spacings: improving upon low discrepancy sequences](https://mlsanity.com/paper/2106.05833/) (2021)

## Built on by (most cited first, 4 of 4)

- [Contextual Strongly Convex Simulation Optimization: Optimize then Predict with Inexact Solutions](https://mlsanity.com/paper/2512.06270/) (2025)
- [Weighted Leave-One-Out Cross Validation](https://mlsanity.com/paper/2505.19737/) (2025)
- [NetworkNet: A Deep Neural Network Approach for Random Networks with Sparse Nodal Attributes and Complex Nodal Heterogeneity](https://mlsanity.com/paper/2604.11673/) (2026)
- [Exploration strategies for Gaussian process bandit optimization with inference regret guarantees](https://mlsanity.com/paper/2610.16187/) (2026)

## Abstract (arXiv)

A design is a collection of distinct points in a given set X, which is assumed to be a compact subset of Rd, and the mesh-ratio of a design is the ratio of its fill distance to its separation radius. The uniformity constant of a sequence of nested designs is the smallest upper bound for the mesh-ratios of the designs. We derive a lower bound on this uniformity constant and show that a simple greedy construction achieves this lower bound. We then extend this scheme to allow more flexibility in the design construction.