A hyperfactorization of order 8, index 2 (Q1182930)

A hyperfactorization of index \(\lambda\) of \(K_{2n}\) is a family of 1- factors such that each pair of nonadjacent edges occur together in exactly \(\lambda\) of the 1-factors. If all the 1-factors are distinct the hyperfactorization is said to be simple. If \(n=4\) and \(\lambda=2\) a simple \(\lambda\)-hyperfactorization does not exist. The author constructs a set of 70 1-factors of \(K_ 8\) that constitute a nonsimple 2- hyperfactorization.