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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.

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