## Some results on $$s^{n-k}$$ fractional factorial designs with minimum aberration or optimal moments.(English)Zbl 0725.62068

Summary: The minimum aberration criterion is commonly used for selecting good fractional factorial designs. In this paper we obtain minimum aberration $$2^{n-k}$$ designs for $$k=3,4$$ and any n. For $$k>4$$ analogous results are not available for general n since the resolution criterion is not periodic for general n and $$k>4$$. However, it can be shown that for any fixed k, both the resolution criterion and the minimum aberration criterion have a periodicity property in n for $$s^{n-k}$$ designs with large n. Furthermore, the optimal-moments criterion is periodic for any n and k.

### MSC:

 62K15 Factorial statistical designs 62K05 Optimal statistical designs
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