  A perfect matroid design (PMD) is a matroid whose flats of the same rank all
have the same size. In this paper we introduce the q-analogue of a PMD and its
properties. In order to do so, we first establish a new cryptomorphic
definition for q-matroids. We show that q-Steiner systems are examples of
q-PMD's and we use this q-matroid structure to construct subspace designs from
q-Steiner systems. We apply this construction to the only known q-Steiner
system, which has parameters S(2,3,13;2), and hence establish the existence of
a new subspace design with parameters 2-(13,4,5115;2).
