Note: A tripling construction for overlarge sets of KTS

An overlarge set of KTS(v), denoted by OLKTS(v), is a collection {([email protected]?{x},B"x):[email protected]?X}, where X is a (v+1)-set, each ([email protected]?{x},B"x) is a KTS(v) and {B"x:[email protected]?X} forms a partition of all triples on X. In this paper, we give a tripling construction for overlarge sets of KTS. 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(3^m(2u+1)) for u=2^2^n^-^1-1 or u=q^n, where prime power q=7 (mod 12) and m>=0,n>=1.