Level permutations of factors can improve space-filling properties of designs, and the properties of the three-level Triple designs constructed by tripling method are related to original designs. In this paper, a new strategy for tripling is provided for constructing three-level uniform designs. By considering all possible level permutations of factors, the relationship is built between the average squared centered \(L_2\)-discrepancy value of the Triple design and the wordlength pattern of the original design, which provides a theoretical basis for selecting a uniform design from an original design with minimum aberration by the level permutations. Moreover, the projection uniformity of the Triple design and its original design is considered, and the relationship of the uniformity pattern between the Triple design and its original design is built. Finally, some numerical results are used to support our theoretical results.

因子的水平排列可以改善设计的空间填充特性，并且通过三重法构造的三层三重设计的特性与原始设计有关。本文为构造三层统一设计提供了一种新的三联策略。通过考虑因子的所有可能的水平排列，可以在以平方为中心的平均平方\（L_2 \）之间建立关系-三重设计的偏差值和原始设计的字长模式，这为从原始设计中选择均匀设计提供了理论基础，该设计的电平偏差最小。此外，考虑了三重设计及其原始设计的投影均匀性，并且建立了三重设计与其原始设计之间的均匀图案的关系。最后，一些数值结果被用来支持我们的理论结果。