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 $L_2$-discrepancy will be investigated. Theoretical result shows that the wrap-around $L_2$-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.

正交阵列已被用于各个领域，因为它具有有吸引力的组合特性。然而，长期以来，组合等效正交阵列被认为是不可区分的，尤其是在建立 ANOVA 模型时。后来，一些论文指出正交数组的排列级别会改变它们的统计推理能力。已推荐标准来评估正交阵列的不同性能。本文提出了一种改进的方法来构造当因子的水平为奇素数和相关环绕性质时的饱和正交阵列。${升}_2$- 差异将被调查。理论结果表明，环绕${升}_2$- 使用修正方法构建的饱和正交阵列的差异小于原始的差异，并且渐近地达到下界。一系列数值例子也证实了所提出方法的有效性。