SOME CLASSES OF ORTHOGONAL LATIN HYPERCUBE DESIGNS

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) is an element of {(24n, 12m), (32n, 16m), (40n, 20m), (48n, 24m), (24n + 1, 12m), (32n + 1, 16m), (40n + 1, 20m), (48n + 1, 24m)}.