Existence results for \(KS_ 3(v;2,4)s\) (Q1088667)

A \(KS_ 3(v;2,4)\) is a (v-1)/2 by (v-1)/2 array so that (1) each of the v points is contained in precisely two cells of each row and each column, (2) each cell is either empty or contains a 3-subset of the v points, and (3) the collection of 3-subsets form the blocks of a (v,3,4)-design. In this paper, the authors show that \(KS_ 3(v;2,4)'s\) exist for \(v\equiv 3 (mod 12)\), \(v\equiv 6 (mod 60)\), and \(v\equiv 9 (mod 96)\). This employs techniques previously used in the construction of doubly resolvable two- fold triple systems, along with some ''doubling'' constructions and small designs.