  In 1985, Janko and Tran Van Trung published an algorithm for constructing
symmetric designs with prescribed automorphisms. This algorithm is based on the
equations by Dembowski (1958) for tactical decompositions of point-block
incidence matrices. In the sequel, the algorithm has been generalized and
improved in many articles.
  In parallel, higher incidence matrices have been introduced by Wilson in
1982. They have proven useful for obtaining several restrictions on the
existence of designs. For example, a short proof of the generalized Fisher's
inequality makes use of these incidence matrices.
  In this paper, we introduce a unified approach to tactical decompositions and
incidence matrices. It works for both combinatorial and subspace designs alike.
As a result, we obtain a generalized Fisher's inequality for tactical
decompositions of combinatorial and subspace designs. Moreover, our approach is
explored for the construction of combinatorial and subspace designs of
arbitrary strength.
