A tripling construction for overlarge sets of KTS

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