Characterization of digital $(0,m,3)$-nets and digital $(0,2)$-sequences in base $2$

We give a characterization of all matrices $A,B,C\in {\mathbb{F}}_2^{m\times m}$ which generate a $(0,m,3)$-net in base $2$ and a characterization of all matrices $B,C\in {\mathbb{F}}_2^{\mathbb{N}\times \mathbb{N}}$ which generate a $(0,2)$-sequence in base $2$.