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Construction of $$2^ m4^ n$$ designs via a grouping scheme. (English) Zbl 0695.62198
Summary: We develop a method for grouping the $$2^ k-1$$ factorial effects in a 2- level factorial design into mutually exclusive sets of the form (s,t,st), where st is the generalized interaction of effects s and t. As an application, we construct orthogonal arrays $$OA(2^ k,2^ m4^ n,2)$$ of size $$2^ k$$, m constraints with 2 levels and n constraints with 4 levels satisfying $$m+3n=2^ k-1$$, and strength 2. The maximum number of constraints with 4 levels in the construction cannot be further improved. In this sense our grouping scheme is optimal. We discuss the advantage of the present approach over other construction methods.

##### MSC:
 62K15 Factorial statistical designs 05B15 Orthogonal arrays, Latin squares, Room squares
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