A tripling construction for overlarge sets of KTS

An overlargeset of KTS(v), denoted by OLKTS(v), is a collection {(X \ {x}, B-x) : x is an element of X}, where X is a (v + 1)-set, each (X \ {x}, B-x) is a KTS(v) and {B-x : x is an element of 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(2n-1)-1 or u = q(n), where prime power q 7 (mod 12) and m >= 0, n >= 1. (C) 2008 Elsevier B.V. All rights reserved.