A new series of large sets of subspace designs over the binary field

In this article, we show the existence of large sets LS_2[3](2,k,v) for infinitely many values of k and v . The exact condition is v ≥ 8 and 0 ≤ k ≤ v such that for the remainders v̅ and k̅ of v and k modulo 6 we have 2 ≤v̅ < k̅≤ 5 . The proof is constructive and consists of two parts. First, we give a computer construction for an LS_2[3](2,4,8) , which is a partition of the set of all 4-dimensional subspaces of an 8-dimensional vector space over the binary field into three disjoint 2- (8, 4, 217)_2 subspace designs. Together with the already known LS_2[3](2,3,8) , the application of a recursion method based on a decomposition of the Graßmannian into joins yields a construction for the claimed large sets.