Space-filling Latin Hypercube Designs based on Randomization Restrictions in Factorial Experiments

TL;DR

This paper introduces a new class of space-filling Latin hypercube designs for factorial experiments, utilizing nearly orthogonal arrays derived from projective geometric structures to improve design properties.

Contribution

It proposes a novel construction of Latin hypercube designs based on nearly orthogonal arrays from projective geometry, enhancing space-filling properties in factorial experiments.

Findings

New class of LHDs based on NOAs from PG(p-1,2)

Improved space-filling properties demonstrated

Connections between geometric structures and experimental design

Abstract

Latin hypercube designs (LHDs) with space-filling properties are widely used for emulating computer simulators. Over the last three decades, a wide spectrum of LHDs have been proposed with space-filling criteria like minimum correlation among factors, maximin interpoint distance, and orthogonality among the factors via orthogonal arrays (OAs). Projective geometric structures like spreads, covers and stars of PG(p-1,q) can be used to characterize the randomization restriction of multistage factorial experiments. These geometric structures can also be used for constructing OAs and nearly OAs (NOAs). In this paper, we present a new class of space-filling LHDs based on NOAs derived from stars of PG(p-1, 2).