Characterization of matrices B such that (I,B,B2) generates a digital net with t-value zero

We study 3-dimensional digital nets over F2 generated by matrices (I,B,B2) where I is the identity matrix and B is a square matrix. We give a characterization of B for which the t-value of the digital net is 0. As a corollary, we prove that such B satisfies B3=I.