Level Permutation Method For Constructing Uniform Designs Under The Wrap-around L₂-discrepancy

In the field of experimental design, the construction of uniform designs attractsmuch attention. The recursive construction via combinatorial design theory and thealgorithmic construction via stochastic optimization are two frequently used methods.However, these two approaches both have considerable defects. Recently, by consid-ering level permutation, Tang et al.（2012） proposed a novel construction method forthree-level uniform designs under the centered L₂-discrepancy （CD） and they have gen-eralized it later. Based on corresponding theories, they constructed uniform designsby doing level permutations to given designs. This method is highly efective as wellas feasible. Similarly a new method for constructing uniform designs under the wrap-around L₂-discrepancy （WD） by permuting levels of factors is provided on this paper.By conducting level permutations of a design, the relationship between the averageWD and generalized wordlength pattern is obtained. On this basis, a general methodfor searching designs with lower WD is proposed. Some special properties of WD canbe used to make our algorithm much more efcient. Numerical results indicate thatour method is better than existing ones.