The objective of this paper is to study the issue of employing the uniformity criterion measured by the wrap-around L2-discrepancy to assess the optimal foldover plans for three-level designs. For three-level fractional factorials as the original designs, the general foldover plan and combined design under a foldover plan are defined, some theoretical properties of the defined foldover plans are obtained, a tight lower bound of the wrap-around L2-discrepancy of combined designs under a general foldover plan is also obtained, which can be used as a benchmark for searching optimal foldover plans. For illustration of the usage of our theoretical results, a catalog of optimal foldover plans for uniform initial designs with s three-level factors is tabulated, where 2 ⩽ s ⩽ 11.

中文翻译：

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三层设计的最佳折叠方案，具有最小的环绕L 2偏差

本文的目的是研究采用通过环绕L2差异测量的均匀性标准来评估三层设计的最佳折叠方案的问题。对于三级分数阶乘因子作为原始设计，定义了总体折叠计划和折叠计划下的组合设计，获得了定义的折叠计划的一些理论性质，组合的环绕L2离散性的下界严格还获得了一般折叠计划下的设计，可以用作搜索最佳折叠计划的基准。为了说明我们的理论结果的用法，列出了具有s三层因子的统一初始设计的最佳折叠方案目录，其中2 s s⩽11。