Statistica Sinica 19 (2009), 1721-1728

A CONSTRUCTION METHOD FOR ORTHOGONAL LATIN

HYPERCUBE DESIGNS WITH PRIME POWER LEVELS

Fang Pang$^1$, Min-Qian Liu$^1$ and Dennis K. J. Lin$^2$

$^1$Nankai University and $^2$The Pennsylvania State University

Abstract: Latin hypercube design (LHD) is popularly used in designing computer experiments. This paper explores how to construct LHDs with $p^d$ ($d=2^c$) runs and up to $(p^d-1)/(p-1)$ factors in which all main effects are orthogonal. This is accomplished by rotating groups of factors in a $p^d$-run regular saturated factorial design. These rotated factorial designs are easy to construct and preserve many attractive properties of standard factorial designs. The proposed method covers the one by Steinberg and Lin (2006) as a special case and is able to generate more orthogonal LHDs with attractive properties. Theoretical properties as well as the construction algorithm are discussed, with an example for illustration.

Key words and phrases: Computer experiment, factorial design, galois field, rotation.