Minimum secondary aberration fractional factorial split-plot designs in terms of consulting designs.

*(English)*Zbl 1123.94010Summary: It is very powerful for constructing nearly saturated factorial designs to characterize fractional factorial (FF) designs through their consulting designs when the consulting designs are small. Mukerjee and Fang employed the projective geometry theory to find the secondary wordlength pattern of a regular symmetrical fractional factorial split-plot (FFSP) design in terms of its complementary subset, but not in a unified form. In this paper, based on the connection between factorial design theory and coding theory, we obtain some general and unified combinatorial identities that relate the secondary wordlength pattern of a regular symmetrical or mixed-level FFSP design to that of its consulting design. According to these identities, we further establish some general and unified rules for identifying minimum secondary aberration, symmetrical or mixed-level, FFSP designs through their consulting designs.

##### MSC:

94B05 | Linear codes (general theory) |

62K15 | Factorial statistical designs |

05A19 | Combinatorial identities, bijective combinatorics |

##### Keywords:

coding theory; consulting design; minimum secondary aberration; fractional factorial split-plot design; projective geometry; wordlength pattern
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\textit{M. Ai} and \textit{R. Zhang}, Sci. China, Ser. A 49, No. 4, 494--512 (2006; Zbl 1123.94010)

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