Some classes of orthogonal Latin hypercube designs

Latin hypercube designs (LHDs) are popularly 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 the new designs presented in this paper, we provide new multiplication methods and further constructions for OLHDs. These constructions lead to new infinite families of OLHD with many factors. For example, we show that when an OLHD(n;m) exists then there also exist OLHDs with (runs; factors) 2 f(24n; 12m), (32n; 16m), (40n; 20m), (48n; 24m), (24n+1; 12m), (32n+1; 16m), (40n+1; 20m), (48n+1; 24m)g. The constructed classes of OLHD are new and are given in this paper for the first time.