A t-[v,k,λ] design in a vector space of dimension v over a finite field is a family of k-subspaces such that each t-subspace is contained in precisely λ elements of this family. They may be considered as a generalization of a spread in a projective space. It is shown that for given t,v,kat-[v,k,λ] design exists for all sufficiently large λ provided the necessary parametric conditions are...