Algorithmic construction of optimal symmetric Latin hypercube designs

We propose symmetric Latin hypercubes for designs of computer experiment. The goal is to offer a compromise between computing effort and design optimality. The proposed class of designs has some advantages over the regular Latin hypercube design with respect to criteria such as entropy and the minimum intersite distance. An exchange algorithm is proposed for constructing optimal symmetric Latin hypercube designs. This algorithm is compared with two existing algorithms by Park (1994. J. Statist. Plann. Inference 39, 95-111) and Morris and Mitchell (1995. J. Statist. Plann. Inference 43, 381-402). Some examples, including a real case study in the automotive industry, are used to illustrate the performance of the new designs and the algorithms.