Classification of Steiner Quadruple Systems of Order 16 and of Rank at Most 13

A Steiner quadruple system SQS($v$) of order $v$ is a 3-design $T(v;4;3;\lambda)$ with $\lambda=1$. In this paper we describe all nonisomorphic systems SQS(16) that can be obtained by the generalized concatenated construction (GC-construction). These Steiner systems have rank at most 13 over $\mathbb F_2$. In particular, there is one system SQS(16) of rank 11 (points and planes of the a fine geometry AG(4;2)), fifteen systems of rank 12, and 4131 systems of rank 13. All these Steiner systems are resolvable.