Further results on overlarge sets of Kirkman triple systems

In this paper, we introduce a new concept . overlarge sets of generalized Kirkman systems (OLGKS), research the relation between it and OLKTS, and obtain some new results for OLKTS. The main conclusion is: If there exist both an OLKF(6k) and a 3-OLGKS(6k.1, 4) for all k .{6,7,., 40}/{8,17,21,22,25,26}, then there exists an OLKTS(v) for any v . 3 (mod 6), v . 21. As well, we obtain the following result: There exists an OLKTS(6u + 3) for u = 22n.1 . 1, 7n, 31n, 127n, 4r25s, where n . 1, r + s . 1.