Partitioning Sets of Quadruples into Designs IT

It is shown that the collection of all \(\binom{9}{4}\) distinct quadruples chosen from a set of nine points can be partitioned into nine mutually disjoint \(3-(8,4,1)\) designs in just two non-isomorphic ways. Two proofs of this result are given: one by direct construction, the other by extending sets of eight mutually disjoint \(2-(7,3,1)\) designs based on a set of eight points.