Parallel-Flats Designs: A Systematic Approach to the Construction of Nested Orthogonal Arrays

Abstract

Recently, nested orthogonal arrays receive notable attention as stepping stones for planning computer simulations with variable levels of accuracy. In this talk, a new class of nested orthogonal arrays, called the nested orthogonal arrays of parallel-flats type, is introduced for addressing this new design issue. Firstly, the sufficient and necessary condition is provided for constructing the proposed designs, then a new class of nested orthogonal arrays is explicitly characterized. Furthermore, a heuristic algorithm is presented for generating designs with small run-sizes, and some analytical methods are developed for constructing large designs through existing small ones. Most interestingly, the size of an obtained design is not necessarily equal to a power of prime. This allows an investigator to planning a series of multi-fidelity computer simulations with a more flexible run-size. In addition, a catalogue of proposed designs with practical run-sizes is presented as a reference for practitioners. Key words: Computer experiment; Golois field; Latin hypercube design; Orthogonal array; Parallel-flats design; Space-filling design.?