Uniform minimum moment aberration designs

This paper discusses the issue of constructing uniform minimum moment aberration designs under discrepancies criteria. By considering all possible level permutations of factors, we establish a linear relationship between power moments and average discrepancy defined by a reproducing kernel for an asymmetrical or symmetrical design. We prove that minimum moment aberration designs often have low average discrepancies. Moreover, the average centered L2-discrepancy is expressed as a linear combination of power moments for a given design. An efficient method for constructing uniform minimum moment aberration designs is proposed. Some asymmetrical uniform minimum moment aberration designs obtained by our method have low centered L2-discrepancy and can be recommended for use in practice.