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 as
also 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.