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The Steiner quadruple systems of order 16
Authors:Petteri Kaski  Patric RJ Östergård  Olli Pottonen
Institution:a Helsinki Institute for Information Technology HIIT, Basic Research Unit, PO Box 68, 00014 University of Helsinki, Finland
b Department of Electrical and Communications Engineering, Helsinki University of Technology, PO Box 3000, 02015 TKK, Finland
Abstract:The Steiner quadruple systems of order 16 are classified up to isomorphism by means of an exhaustive computer search. The number of isomorphism classes of such designs is 1,054,163. Properties of the designs—including the orders of the automorphism groups and the structures of the derived Steiner triple systems of order 15—are tabulated. A consistency check based on double counting is carried out to gain confidence in the correctness of the classification.
Keywords:Classification  Derived design  SQS  Steiner system
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