Factorial designs and the theory of trade-off

We consider a method to construct factorial designs with all factors at two levels and with an information matrix, pertaining to a specified model, that is equal to the information matrix for a given design. The method is based on a relation between this problem and the problem of trade-off in block designs. By exploring this relation, the extensive results on t-trades can be used for the construction of the desired factorial designs. This provides also additional incentive for the continued development of the theory of trade-off.