Partitioning Sets of Quadruples into Designs IT

Abstract

It is shown that the collection of all $(\genfrac{}{}{0ex}{}{9}{4})$ 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.