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 R^d 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.
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Luc Pronzato. Minimax and maximin space-filling designs: some properties and methods for construction. Journal de la Société Française de Statistique, Société Française de Statistique et Société Mathématique de France, 2017, 158 (1), pp.7-36. ⟨www.sfds.asso.fr/journal⟩. ⟨hal-01496712⟩

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