Tang, Boxin; Wu, C. F. J. Characterization of minimum aberration \(2^{n-k}\) designs in terms of their complementary designs. (English) Zbl 0867.62068 Ann. Stat. 24, No. 6, 2549-2559 (1996). Summary: A general result is obtained that relates the word-length pattern of a \(2^{n-k}\) design to that of its complementary design. By applying this result and using group isomorphism, we are able to characterize minimum aberration \(2^{n-k}\) designs in terms of properties of their complementary designs. The approach is quite powerful for small values of \(2^{n-k}-n-1\). In particular, we obtain minimum aberration \(2^{n-k}\) designs with \(2^{n-k}-n-1=1\) to 11 for any \(n\) and \(k\). Cited in 3 ReviewsCited in 49 Documents MSC: 62K15 Factorial statistical designs 62K05 Optimal statistical designs Keywords:minimum aberration designs; fractional factorials; Hamming code; isomorphic designs; MacWilliams identities; word-length pattern; group isomorphism; complementary designs × Cite Format Result Cite Review PDF Full Text: DOI References: [1] BOX, G. E. P. and HUNTER, J. S. 1961. The 2 fractional factorial designs. Technometrics 3 311 351, 449 458. Z. · Zbl 0100.14406 [2] BOX, G. E. P., HUNTER, W. G. and HUNTER, J. S. 1978. Statistics for Experimenters. Wiley, New York. Z. n m Z. · Zbl 0394.62003 [3] CHEN, H. and HEDAy AT, A. S. 1996. 2 fractional factorial designs with weak minimum aberration. Ann. Statist. 24 2536 2548. · Zbl 0867.62066 · doi:10.1214/aos/1032181167 [4] CHEN, J. 1990. On minimum aberration fractional factorial designs. Ph.D. dissertation, Dept. Statistics, Univ. Wisconsin, Madison. Z. n k CHEN, J. 1992. Some results on 2 fractional factorial designs and search for minimum aberration designs. Ann. Statist. 20 2124 2141. Z. · Zbl 0770.62063 · doi:10.1214/aos/1176348907 [5] CHEN, J., SUN, D. X. and WU, C. F. J. 1993. A catalogue of two-level and three-level fractional factorial designs with small runs. Internat. Statist. Rev. 61 131 145. Z. n k · Zbl 0768.62058 · doi:10.2307/1403599 [6] CHEN, J. and WU, C. F. J. 1991. Some results on s fractional factorial designs with minimum aberration or optimal moments. Ann. Statist. 19 1028 1041. Z. n m · Zbl 0725.62068 · doi:10.1214/aos/1176348135 [7] FRANKLIN, M. F. 1984. Constructing tables of minimum aberration p designs. Technometrics 26 225 232. Z. k p JSTOR: · doi:10.2307/1267548 [8] FRIES, A. and HUNTER, W. G. 1980. Minimum aberration 2 designs. Technometrics 22 601 608. Z. JSTOR: · Zbl 0453.62063 · doi:10.2307/1268198 [9] PLESS, V. 1982. Introduction to the Theory of Error-Correcting Codes. Wiley, New York. · Zbl 0481.94004 [10] OTTAWA, ONTARIO ANN ARBOR, MICHIGAN 48109-1027 CANADA K1A OT6 E-MAIL: jeffwu@stat.lsa.umich.edu This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.