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

• Published in: Journal of approximation theory Vol. 294; p. 105931
• Main Authors: Pronzato, L., Zhigljavsky, A.
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01-10-2023; Elsevier
• Subjects: Covering radius; Fill distance; Greedy algorithm; Mathematics; Mesh norm; Mesh-ratio; Packing radius; Quasi-uniform design; Separation radius; Statistics; Quasi-uniform design; Fill distance; Covering radius; Mesh norm; Greedy algorithm; Packing radius; Separation radius; Mesh-ratio
• ISSN: 0021-9045; 1096-0430
• DOI: 10.1016/j.jat.2023.105931

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.