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On the coset pattern matrices and minimum $$M$$-aberration of $${2^{n-p}}$$ designs. (English) Zbl 1086.62086
Summary: The coset pattern matrix (CPM) is formally defined as an elaborate characterization of the aliasing patterns of a fractional factorial design. The possibility of using CPM to check design isomorphism is investigated. Despite containing much information about effect aliasing, the CPM fails to determine a design uniquely. We report and discuss small nonisomorphic designs that have equivalent coset pattern matrices. These examples imply that the aliasing property and the combinatorial structure of a design depend on each other in a complex manner. Based on CPM, a new optimality criterion, called the minimum $$M$$-aberration criterion, is proposed to rank-order designs. Its connections with other existing optimality criteria are discussed.

MSC:
 62K15 Factorial statistical designs 62K05 Optimal statistical designs