Construction of (nearly) orthogonal sliced Latin hypercube designs

Sliced Latin hypercube designs have found a wide range of applications. Such a design is a special Latin hypercube design that can be partitioned into slices which are still LHDs when the levels of each slices are collapsed properly. In this paper we propose a method for constructing sliced Latin hypercube designs with second-order orthogonality. The resulting designs are further augmented to be nearly orthogonal sliced Latin hypercube designs which have much more columns. Also, two methods of generating nearly orthogonal sliced Latin hypercube designs are proposed. The methods are convenient, efficient and capable of accommodating any number of slices.