Abstract
Orthogonal array has been used in various fields, as it possesses attractive combinatorial properties. However, for a long time, combinatorially equivalent orthogonal arrays are thought to be indistinguishable, especially when an ANOVA model is established. Later on, some papers pointed out that permuting levels of orthogonal arrays will alter their statistical inference abilities. Criteria have been recommended for evaluating the different performance of orthogonal arrays. In this paper, a revised method is proposed to construct saturated orthogonal arrays when the level of the factors is an odd prime and properties of the related wrap-around L2-discrepancy will be investigated. Theoretical result shows that the wrap-around L2-discrepancies of the saturated orthogonal arrays constructed using the revised method are less than those of the original ones, and asymptotically attain the lower bounds. A series of numerical examples also confirms the effectiveness of the proposed method.
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