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 F 2 . 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 ( mod 8 ) .