Classical mixed partitions

Through a method given in [3], a mixed partition of PG(2n− 1, q2) can be used to construct a (2n− 1)-spread of PG(4n− 1, q) and, hence, a translation plane of order q2n. A mixed partition in this case is a partition of the points of PG(2n− 1, q2) into PG(n− 1, q2)’s and PG(2n− 1, q)’s which we call Baer subspaces. In this paper, we completely classify the mixed partitions which generate regular spreads and, hence, can be classified as classical.