Some characterizations of affinely full-dimensional factorial designs

A new class of two-level non-regular fractional factorial designs is defined. We call this class an affinely full-dimensional factorial design, meaning that design points in the design of this class are not contained in any affine hyperplane in the vector space over F2. The property of the indicator function for this class is also clarified. A fractional factorial design in this class has a desirable property that parameters of the main effect model are simultaneously identifiable. We investigate the property of this class from the viewpoint of D-optimality. In particular, for the saturated designs, the D-optimal design is chosen from this class for the run sizes r≡5,6,7(mod8).