Classification of steiner quadruple systems of order 16 and rank 14

A Steiner quadruple system S(v, 4, 3) of order v is a 3-design T (v, 4, 3, λ) with λ = 1. In the previous paper [1] we classified all such Steiner systems S(16, 4, 3) of order 16 with rank 13 or less over F 2. In particular, we have proved that there is can be obtained by the generalized doubling construction, which we give here. Our main result is that there are exactly 684764 non-isomorphic Steiner quadruple systems S(16, 4, 3) of order 16 with rank 14. We found all non-isomorphic homogenious systems with rank 14 over F 2. * The paper has been written under the partial financial support of the Russian fund for the fundamental research (the number of project 03-01-00098)