The spectrum of balanced P^(3)(1; 5)-designs

Given a 3-uniform hypergraph H^(3), an H^(3)-decomposition of the complete hypergraph K^(3)_v is a collection of hypergraphs, all isomorphic to H^(3), whose edge sets partition the edge set of K^(3)_v . An H_(3)-decomposition of K_(3)_v is also called an H^(3)-design and the hypergraphs of the partition are said to be the blocks. An H^(3)-design is said to be balanced if the number of blocks containing any given vertexof K^(3)_v is a constant. In this paper, we determine completely, without exceptions, the spectrum of balanced P^(3)(1; 5)-designs.