By using level permutation technique,the calculation formula of average centered L2-discrepancy for mixed two and three levels U-type designs is given,and a detailed proof is also provided.Based on this formula,connections between average centered L2-discrepancy and GMA criterion、orthogonality criterion,and a lower bound for average centered L2-discrepancy are derived.Finally,a numerical example is presented to verify that the lower bound is tight.
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