Large sets of extended directed triple systems with odd orders

For three types of triples, unordered, cyclic and transitive, the corresponding extended triple, extended triple system and their large set are introduced. The spectrum of L E D T S ( v ) for even v has been given in our paper (Liu and Kang (2009) [9]). In this paper, we shall discuss the existence problem of L E D T S ( v ) for odd v and give the almost complete conclusion: there exists an L E D T S ( v ) for any positive integer v ≠ 4 except possible v = 95 , 143 , 167 , 203 , 215 .