For an orthogonal array (or fractional factorial design) on k factors, Xu and Wu (2001) define the array's generalized wordlength pattern (A1,..., Ak), by relating a cyclic group to each factor. They prove the property that the array has strength t if and only if A1 = ··· = A t = 0. In their 2012 paper, Beder and Beder show that this result is independent of the group structure used. Non-abelian groups can be used if the assumption is made that the groups Gi are chosen so that the counting function O of the array is a class function on G. The aim of this thesis is to construct examples of orthogonal arrays on G = G 1 x ··· x Gk, where G is non-abelian, having two properties: given strength, and counting function O that is constant on the conjugacy classes of G..
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机译:对于基于k个因子的正交数组(或分数阶乘设计),Xu和Wu(2001)通过将循环组与每个因子相关联来定义该数组的广义字长模式(A1,...,Ak)。他们证明了只有当A1 =···= A t = 0时,数组才具有强度t的性质。Beder和Beder在2012年的论文中表明,该结果与所使用的组结构无关。如果假设选择了Gi组,则可以使用非阿贝尔群,这样数组的计数函数O是G的类函数。本文的目的是构造G = G的正交数组的示例1 x X Gk,其中G是非阿贝尔的,具有两个属性:给定强度和对G的共轭类恒定的计数函数O。
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