Balanced P(3)(2; 4)-designs

Given an hypergraph H(3), uniform of rank 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 H(3)-designs.