Construction of Latin hypercube designs with nested and sliced structures

Recently, the construction of nested or sliced Latin hypercube designs (LHDs) has received notable interest for planning computer experiments with special combinational structures. In this paper, we propose an approach to constructing nested and/or sliced LHDs by using small LHDs and structural vectors/matrices. This method is easy to implement, and can generate nested and sliced LHDs through a unified algorithm. Moreover, an algorithm for improving the space-filling properties of the resulting designs is developed, and under some control the orthogonality of the constructed designs are attainable. Some examples are provided for illustrating the proposed algorithms.