On the number of indecomposable block designs

A t-(v; k;) design D is a system (multiset) of k-element subsets (called blocks) of a v-element set V such that every t-element subset of V occurs exactly times in the blocks of D. A t-(v; k;) design D is called inde-composable (or elementary) if and only if there is no subsystem which is a t-(v; k; 0) design with 0 < 0 <. It is known that the number of inde-composable designs for given parameters t; v; k is nite. A block design is a t-(v; k;) design with t = 2. The exact number of non-isomorphic, indecom-posable block designs is only known for k = 3 and v 7. We computed the number of indecomposable designs for v 13 and 6. The algorithms used will be described.