A new and flexible method for constructing designs for computer experiments

TL;DR

This paper introduces a versatile method for constructing high-quality designs for computer experiments by building large designs from smaller ones, successfully solving the existence problem for orthogonal Latin hypercubes.

Contribution

The paper presents a novel, flexible approach for designing experiments, specifically solving the existence problem for orthogonal Latin hypercubes and enabling construction of various related designs.

Findings

Complete solution to the existence problem of orthogonal Latin hypercubes.

Explicit construction method for large orthogonal Latin hypercubes from small ones.

Adaptability of the method to create nearly orthogonal and cascading Latin hypercubes.

Abstract

We develop a new method for constructing "good" designs for computer experiments. The method derives its power from its basic structure that builds large designs using small designs. We specialize the method for the construction of orthogonal Latin hypercubes and obtain many results along the way. In terms of run sizes, the existence problem of orthogonal Latin hypercubes is completely solved. We also present an explicit result showing how large orthogonal Latin hypercubes can be constructed using small orthogonal Latin hypercubes. Another appealing feature of our method is that it can easily be adapted to construct other designs; we examine how to make use of the method to construct nearly orthogonal and cascading Latin hypercubes.