Minimax and maximin space-filling designs: some properties and methods for construction

Abstract

A few properties of minimax and maximin optimal designs in a compact subset of Rd are presented, and connections with other space-filling constructions are indicated. Several methods are given for the evaluation of the minimax-distance (or dispersion) criterion for a given n-point design. Various optimisation methods are proposed and their limitations, in particular in terms of dimension d, are indicated. A large majority of the results presented are not new, but their collection in a single document containing a respectable bibliography will hopefully be useful to the reader.