Construction of S(3) (2, 3)-Designs of Any Index

Let H(3) be a uniform hypergraph of rank 3. A hyperstar S(3)(2,3) of centre C={x,y} is a 3-uniform hypergraph with three hyperedges, all having the centre C={x,y} in common, with x and y of degree 3 and the remaining vertices of degree 1. In this paper, we determine the spectrum of S(3)(2,3)-designs for any index λ.