Large sets of t-designs over finite fields

A t - ( n , k , λ ; q ) -design is a set of k-dimensional subspaces, called blocks, of an n-dimensional vector space V over the finite field with q elements such that each t-dimensional subspace is contained in exactly λ blocks. A partition of the complete set of k-dimensional subspaces of V into disjoint t - ( n , k , λ ; q ) designs is called a large set of t-designs over finite fields. In this paper we give the first nontrivial construction of such a large set with t ⩾ 2 .