A new rotation method for constructing orthogonal Latin hypercube designs

Latin hypercube designs(LHDs) are very popular in designing computer experiments. In addition,orthogonality is a desirable property for LHDs, as it allows the estimates of the main effects in linear models to be uncorrelated with each other, and is a stepping stone to the space-filling property for fitting Gaussian process models. Among the available methods for constructing orthogonal Latin hypercube designs(OLHDs),the rotation method is particularly attractive due to its theoretical elegance as well as its contribution to spacefilling properties in low-dimensional projections. This paper proposes a new rotation method for constructing OLHDs and nearly OLHDs with flexible run sizes that cannot be obtained by existing methods. Furthermore,the resulting OLHDs are improved in terms of the maximin distance criterion and the alias matrices and a new kind of orthogonal designs are constructed. Theoretical properties as well as construction algorithms are provided.