Construction of orthogonal general sliced Latin hypercube designs

Computer experiments have attracted increasing attention in recent decades. General sliced Latin hypercube design (LHD), which is a sliced LHD with multiple layers and at each layer of which each slice can be further divided into smaller LHDs at the above layer, is widely applied in computer experiments with qualitative and quantitative factors, multiple model experiments, cross-validation, and stochastic optimization. Orthogonality is an important property for LHDs. Methods for constructing orthogonal and nearly orthogonal general sliced LHDs are put forward first time in this paper, where orthogonal designs and structural vectors are used in the constructions. The resulting designs not only possess orthogonality in the whole designs, but also achieve orthogonality in each layer before and after being collapsed. Furthermore, based on different structural vectors, the methods can be easily extended to construct orthogonal LHDs with some desired sliced or nested structures.