Statistica Sinica 24 (2014), 101-120

SOME CLASSES OF ORTHOGONAL LATIN HYPERCUBE

DESIGNS

Stelios D. Georgiou and Ifigenia Efthimiou

University of the Aegean

Abstract: Latin hypercube designs (LHDs) are commonly used in designing computer experiments. A number of methods have been proposed to construct LHDs with orthogonality among the main-effects. In this paper, we propose a new method for constructing orthogonal LHDs (OLHDs) with $12$, $16$, $20$, and $24$ factors having a flexible run size. Moreover, using these designs we provide new multiplication methods and further constructions for OLHDs. These constructions lead to infinite families of OLHD with many factors. For example, we show that when an $OLHD(n, m)$ exists, there also exist OLHDs with $(runs, factors)\in \{(24n,12m)$, $(32n,16m)$, $(40n,20m)$, $(48n,24m)$, $(24n + 1,12m)$, $(32n + 1,16m)$, $(40n + 1,20m)$, $(48n + 1,24m)\}$.

Key words and phrases: Circulant matrices, computer experiments, orthogonal Latin hypercube design, periodic autocorrelation function.