A tripling construction for overlarge sets of KTS

An overlarge set   of KTS(v), denoted by OLKTS(v), is a collection {(X∖{x},Bx):x∈X}{(X∖{x},Bx):x∈X}, where XX is a (v+1)(v+1)-set, each (X∖{x},Bx)(X∖{x},Bx) is a KTS(v) and {Bx:x∈X}{Bx:x∈X} forms a partition of all triples on XX. In this paper, we give a tripling construction for overlarge sets of KTSKTS. Our main result is that: If there exists an OLKTS(v) with a special property, then there exists an OLKTS(3v). It is obtained that there exists an OLKTS(3m(2u+1)) for u=22n−1−1u=22n−1−1 or u=qnu=qn, where prime power q≡7q≡7 (mod 12) and m≥0,n≥1m≥0,n≥1.