On the character of the depth of a lattice of closed classes of nonhomogeneous functions

The closed classes of non-homogeneous functions
$$ f\colon\{\{0,1\}{}^{n}\times\{0,3\}{}^{m}\} \rightarrow \{0,1\} $$
are studied up to the coincidence of trace consisting of all Boolean functions entering these classes. The admissible combinations of capacities for such classes are described under fixed depth of the traces of the classes in the Post lattice.