Abstract
Four general classes of partially balanced designs for 2
n
factorials, corresponding to four different forms of a general null hypothesis H on factorial effects, are presented. For the typical design in each class, the simplified form of the non-centrality parameter λ
2
of the asymptotic chi-square distribution of the likelihood ratio statistic for testing the corresponding form of H
0
is derived under defined local alternatives. Optimal designs d
1
maximizing λ
2
in the i-th class and minimizing the trace, determinant and largest eigenvalue of a defined covariance matrix, i =1,...,4, are determined.