  We introduce a hybridization of digital sequences with uniformly distributed
sequences in the domain of $b$-adic integers, $\mathbb Z_{b}, b\in\mathbb
N\setminus\{1\}$, by using such sequences as input for generating matrices. The
generating matrices are then naturally required to have finite row-lengths. We
exhibit some relations of the `classical' digital method to our extended
version, and also give several examples of new constructions with their
respective quality assessments in terms of $t,\mathbf T$ and discrepancy.
