**Sankhya:
The Indian Journal of Statistics**

2004, Volume 66, Pt. 2, 343--361

**GA-optimal Balanced Fractional
$2^m$ Factorial Designs of Resolution $R^*( \{0,1 \}|3)$**

Masahide Kuwada , Hiroshima University, Higashi-Hiroshima,
Japan

Yoshifumi Hyodo , Okayama University of Science, Okayama, Japan

Hiromu Yumiba , International Institute for Natural Sciences, Kurashiki, Japan

SUMMARY. Using the algebraic structure of the triangular multidimensional partially balanced association scheme and a matrix equation, we give a balanced fractional $ 2^{m}$ factorial design derived from a simple array such that the general mean and all the main effects are estimable, where the four-factor and higher-order interactions are assumed to be negligible. We also give optimal designs with respect to the generalized A-optimality criterion for $ 6\le m\le8$ when the number of assemblies is less than the number of non-negligible factorial effects.

*AMS (1991) subject classification. 62K05, 62K15, 05B30.*

*Key words and phrases. *Association algebra, GA-optimality criterion, parametric
functions, resolution, simple arrays.