Latin Matchings and Ordered Designs OD(n−1, n, 2n−1)

This paper revisits a combinatorial structure called the large set of ordered design (LOD). Among others, we introduce novel Latin matching and prove that order n leads to an LOD(n−1, n, 2n−1); thus, obtain constructions for LOD(1, 2, 3), LOD(2, 3, 5), LOD(4, 5, 9). Moreover, show constructing is at least as hard Steiner system S(n−2, n−1, 2n−2); therefore, must be prime. We also some applications in multiagent systems.