【摘要】 针对构成三水平等距设计D的一组互补设计d,■和tripling得到的Triple设计T（d）,■，讨论了子设计■和其补设计d的Triple设计T（d）之间的关系，建立了子设计d的Triple设计T（d）的可卷型L₂-偏差与其补设计■的字长型模式之间的关系，并且给出了设计T（d）与■之间的字长型模式的解析关系，最后基于可卷型L₂-偏差讨论了设计T （d）与■之间的均匀性关系并获得了相应的下界.这些关系为利用较少因子、较少试验研究较多因子、较多试验设计的性质提供了理论基础.更多还原

【Abstract】 For the complementary designs d,■ composed of a three-level equidistant designs D and their Triple designs T（d）,■ by tripling,the relationship between the subdesign ■ and the Triple design of its complementary design T（d） is considered,the relationship between the wrap-around L₂-discrepancy of the Triple design of d denoted by T（d） and the generalized wordlength pattern of the complementary design of d denoted by ■ is built.Moreover the analytical connection of the generalized wordlength pattern between T（d） and ■ is presented. The relationship of uniformity between ■ and T（d） is discussed,and the lower bounds of such designs are obtained based on the wrap-around L₂-discrepancy. These results obtained provide theoretical basis for studying the properties of the design with more factors,more runs by the design with fewer factors,fewer runs.更多还原