Lattice-based designs possessing quasi-optimal separation distance on all projections

TL;DR

This paper introduces a theoretical framework for creating lattice-based experimental designs that achieve near-optimal separation distances across all projections, enhancing space-filling properties for computer experiments.

Contribution

It develops a novel approach using lattice rotations to generate designs with quasi-optimal separation and fill distances, outperforming existing designs.

Findings

Densest packing-based maximum projection designs outperform existing designs.

The framework enables systematic generation of designs with desirable space-filling properties.

R package LatticeDesign provides tools for practical implementation.

Abstract

Experimental designs that spread out points apart from each other on projections are important for computer experiments when not necessarily all factors have substantial influence on the response. We provide a theoretical framework to generate designs that possess quasi-optimal separation distance on all of the projections and quasi-optimal fill distance on univariate margins. The key is to use special techniques to rotate certain lattices. One such type of design is densest packing-based maximum projection designs, which outperform existing types of space-filling designs in many scenarios. Computer code to generate these designs is provided in R package LatticeDesign.