The minimum volume of subspace trades

A subspace bitrade of type Tq(t, k, v) is a pair (T0, T1) of two disjoint nonempty collections (trades) of k-dimensional subspaces of a v-dimensional space F v over the finite field of order q such that every t-dimensional subspace of V is covered by the same number of subspaces from T0 and T1. In a previous paper, the minimum cardinality of a subspace Tq(t, t + 1, v) bitrade was establish. We generalize that result by showing that for admissible v, t, and k, the minimum cardinality of a subspace Tq(t, k, v) bitrade does not depend on k.