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- design by computer, which corresponds to a halving . The application of the new recursion method to this halving and an already known yields two infinite two-parameter series of halvings and with integers , and , .
Thus in particular, two new infinite series of nontrivial subspace designs with are constructed. Furthermore as a corollary, we get the existence of infinitely many nontrivial large sets of subspace designs with .