Classification of Steiner quadruple systems of order 16 and rank at most 131

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A Steiner quadruple system SQS(v) of order v is a 3-design T (v, 4, 3, ?) with ? = 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.