Sliced Latin hypercube designs with arbitrary run sizes

Latin hypercube designs achieve optimal univariate stratifications and are useful for computer experiments. Sliced Latin hypercube designs are Latin hypercube designs that can be partitioned into smaller Latin hypercube designs. In this work, we give, to the best of our knowledge, the first construction of sliced Latin hypercube designs that allow arbitrarily chosen run sizes for the slices. We also provide an algorithm to reduce correlations of our proposed designs.