We give a complete classification of all matrices C1,C2,C3 ∈ {C_3} \in \mathbb{F}_2^{m \times m} which generate a digital (0,m, 3)-net in base 2 and a complete classification of all matrices C1,C2 ∈ {C_2} \in \mathbb{F}_2^{\mathbb{N} \times \mathbb{N}} which generate a digital (0, 2)-sequence in base 2.