  Let K be an arbitrary (commutative) field with at least three elements, and
let n, p and r be positive integers with r<=min(n,p). In a recent work, we have
proved that an affine subspace of M_{n,p}(K) containing only matrices of rank
greater than or equal to r must have a codimension greater than or equal to
(r+1)r/2. Here, we classify, up to equivalence, these subspaces with the
minimal codimension (r+1)r/2. This uses our recent classification of the affine
subspaces of M_r(K) contained in GL_r(K) and which have the maximal dimension
r(r-1)/2.
