This paper investigates the distribution properties of subsequences of digital sequences and their hybrid version for the special case of finite-row generating matrices and states new criterions on the index sequence which can be used to decide the uniform distribution of the corresponding subsequence. These criterions are related to earlier ones and they are applied to previously considered examples. Furthermore, a detailed study of power residues in different congruence classes is carried out, which together with the new criterions allows to give a full classification of all finite-row generating matrices that yield uniformly distributed subsequences if they are indexed by a sequence (np)n≥0 of fixed prime exponent.