On large sets of Kirkman triple systems and 3-wise balanced design Original Research Article

In this paper, the existence of large sets of Kirkman triple system is transformed to the existence of finite OLKFs and LGKSs. Our main result is: If there exist both an OLKF(6k) and an LGKS({3},{6+3},6k−1,6(k−1)+3,3) for all k∈{6,7,…,40}⧹{14,17,21,22,25,26}, then there exists an LKTS(v) for any v≡3 (mod 6), v≠21. As well, we present a construction of 3-wise balanced design.