New infinite families of simple q-analogs of group divisible designs with arbitrary block dimension are obtained from the incidence matrix of 2-subspaces and k-subspaces under the GL(m, q^l) action, together with a recursive construction for q-analogs of pairwise balanced designs.
Drudge, On the orbits of Singer groups and their subgroups, Electron
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New infinite families of $q$-analogs of group divisible designs with arbitrary block dimension
New infinite families of simple q-analogs of group divisible designs with arbitrary block dimension are obtained from the incidence matrix of 2-subspaces and k-subspaces under the GL(m, q^l) action, together with a recursive construction for q-analogs of pairwise balanced designs.