# zbMATH — the first resource for mathematics

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