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

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. & COPY; 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).