Efficient Algorithmic Construction of Designs

A t-(v,k,~) design is a system of (not necessarily distinct) k-element subsets (called blocks) of a v-element set K such that every t-element subset of K appears exactly ~ times in the blocks. Two t-(v,k,~) designs ~ and N are called isomorphic if and only if there is a permutation of the elements of K which bijectively transforms M into N. A t-(v,k,~) design B is called indecomposable if and only if there is no subsystem B' of B which is a t-(v,k,~') design for 0 ~ ~'~ ~. The existence of a t-(v,k,~) design implies that