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Construction of asymmetrical orthogonal arrays of the type \(OA(s^ k, s^ m(s^{r_ 1})^{n_ 1} \cdots(s^{r_ t})^{n_ t})\). (English) Zbl 0822.62063
Summary: We extend the grouping scheme introduced by the first author [Ann. Stat. 17, No. 4, 1880-1885 (1989; Zbl 0695.62198)] and construct a class of saturated asymmetrical orthogonal arrays of the type \(OA (s^ k, s^ m(s^ r)^ n)\), where \(s\) is a prime power and \(r\) is any positive integer. The method is generalized to construct \(OA (s^ k, s^ m (s^{r_ 1})^{n_ 1} \cdots (s^{r_ t})^{n_ t})\) for any prime power \(s\), any positive integer \(r_ j\), and some combinations of \(m\) and \(n_ j\).

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