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

Abstract

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(6^k) and an LGKS({3},{6+3},6^k−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 $\text{v≡3}\text{(}\text{mod}\text{6)}$, v≠21. As well, we present a construction of 3-wise balanced design.