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