On large sets of disjoint Kirkman triple systems Original Research Article

In this paper, we introduce LR(u) designs and use these designs together with large sets of Kirkman triple systems (LKTS) and transitive KTS (TKTS) of order v to construct an LKTS(uv). Our main result is that there exists an LKTS(v) for v∈{3nm(2·13k+1)t;n⩾1, k⩾1, t=0,1, m∈{1,5,11,17,25,35,43}}.