A class of constructions for turán's (3, 4)-problem

Let f(n) denote the minimal number of edges of a 3-uniform hypergraph G=(V, E) on n vertices such that for every quadruple Y ⊂V there exists Y ⊃e ∈E. Turán conjectured that f(3 k)=k(k-1)(2 k-1). We prove that if Turán's conjecture is correct then there exist at least 2 ^k-2 non-isomorphic extremal hypergraphs on 3 k vertices.