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(6 (k) ) and a 3-OLGKS(6 (k-1), 4) for all k a{6,7,aEuro broken vertical bar, 40}/{8,17,21,22,25,26}, then there exists an OLKTS(v) for any v equivalent to 3 (mod 6), v not equal 21. As well, we obtain the following result: There exists an OLKTS(6u + 3) for u = 2(2n-1) - 1, 7n, 31 (n) , 127 (n) , 4(r)25 (s) , where n a parts per thousand yen 1, r + s a parts per thousand yen 1.