Large sets of subspace designs

In this article, three types of joins are introduced for subspaces of a vector space. Decompositions of the Graßmannian into joins are discussed. This framework admits a generalization of large set recursion methods for block designs to subspace designs.We construct a 2-(6,3,78)5 design by computer, which corresponds to a halving LS5[2](2,3,6). The application of the new recursion method to this halving and an already known LS3[2](2,3,6) yields two infinite two-parameter series of halvings LS3[2](2,k,v) and LS5[2](2,k,v) with integers v≥6, v≡2(mod4) and 3≤k≤v−3, k≡3(mod4).Thus in particular, two new infinite series of nontrivial subspace designs with t=2 are constructed. Furthermore as a corollary, we get the existence of infinitely many nontrivial large sets of subspace designs with t=2.