Asymmetric fractional factorial plans optimal for main effects and specified two-factor interactions

Fractional factorial plans for asymmetric factorial experiments are obtained. These are shown to be universally optimal within the class of all plans involving the same number of runs under a model that includes the mean, all main effects and a specified set of two-factor interactions. Finite projective geometry is used to obtain such plans for experiments wherein the number of levels of each of the factors and the number of runs is a power of m, a prime or a prime power. Methods of construction of optimal plans under the same model are also discussed for the case where the number of levels as well as the number of runs are not necessarily powers of a prime number.