Some results on minimum aberration mixed-level \((2^\gamma)2^n\) factorial designs. (English) Zbl 1174.62476
Summary: In this paper, by introducing the concept of consulting designs and based on the connection between factorial design theory and coding theory, the authors obtain some combinatorial identities that relate the word length pattern of a regular mixed-level \((2^\gamma)2^n\) factorial to that of its consulting design. Consequently, a general rule for identifying minimum aberration \((z^\gamma)z^n\) factorial designs through their consulting designs is established. This is an improvement and generalization of the related results of R. Mukerjee and C.F.J. Wu [Stat. Sin. 11, No. 1, 225–239 (2001; Zbl 0967.62054)]
MSC:
62K15 | Factorial statistical designs |
68P30 | Coding and information theory (compaction, compression, models of communication, encoding schemes, etc.) (aspects in computer science) |