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 vertex of K(3) v is a constant. In this paper, we determine completely, without exceptions, the spectrum of balanced P(3)(1; 5)-designs.