Interleaved lattice-based maximin distance designs

TL;DR

This paper introduces a novel method for constructing interleaved lattice-based maximin distance designs that are highly effective in multiple dimensions, especially useful for computer experiments with prior knowledge of variable importance.

Contribution

The paper presents a new lattice-based approach for maximin distance designs that outperform existing methods in four or more dimensions, adaptable to various distance measures.

Findings

Designs exhibit interleaved-layer structures

Achieve superior maximin distances in higher dimensions

Applicable to weighted and unweighted distance measures

Abstract

We propose a new method to construct maximin distance designs with arbitrary number of dimensions and points. The proposed designs hold interleaved-layer structures and are by far the best maximin distance designs in four or more dimensions. Applicable to distance measures with equal or unequal weights, our method is useful for emulating computer experiments when a relatively accurate priori guess on the variable importance is available.