On the BIB design having the minimum p-rank

AbstractIt is shown that (i) among BIB designs with parameters (2t+1 − 1, 2t+1 − 1, 2t − 1, 2t − 1, 2t−1 − 1), the incidence matrix of the BIB design PG(t, 2):t − 1 derived from a finite projective geometry PG(t, 2) has the minimum 2-rank and (ii) among BIB designs with parameters (2t, 2t+1 − 2, 2t − 1, 2−1, 2t−1 − 1), the incidence matrix of the BIB design EG(t, 2):t − 1 derived from an affine geometry EG(t, 2) has the minimum 2-rank