Bi-directional sliced Latin hypercube designs

We propose a new type of design for computer experiments called bidirectional sliced Latin hypercube design (BSLHD). The proposed design is a special Latin hypercube design (LHD) that simultaneously accommodates two slicing structures. It consists of multiple LHDs of smaller sizes, which can be joined in alternative ways to form two sets of standard sliced LHDs. These new structures are useful for computer experiments with qualitative factors, experiments running in batch mode, and ensembles of multiple computer models. Some sampling properties of the designs in estimating function means are proved and illustrated through numerical examples.