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.
@article{1032181168,
author = {Tang, Boxin and Wu, C. F. J.},
title = {Characterization of minimum aberration $2\sp {n-k}$ designs in terms of their complementary designs},
journal = {Ann. Statist.},
volume = {24},
number = {6},
year = {1996},
pages = { 2549-2559},
language = {en},
url = {http://dml.mathdoc.fr/item/1032181168}
}
Tang, Boxin; Wu, C. F. J. Characterization of minimum aberration $2\sp {n-k}$ designs in terms of their complementary designs. Ann. Statist., Tome 24 (1996) no. 6, pp. 2549-2559. http://gdmltest.u-ga.fr/item/1032181168/