Glasnik Matematicki, Vol. 58, No. 2 (2023), 233-245. \( \)

STEINER TRIPLE SYSTEMS OF ORDER \(21\) WITH SUBSYSTEMS

Daniel Heinlein and Patric R. J. Östergård

Department of Information and Communications Engineering, Aalto University, 00076 Aalto, Finland
e-mail:-

Department of Information and Communications Engineering, Aalto University, 00076 Aalto, Finland
e-mail:patric.ostergard@aalto.fi

Abstract.   The smallest open case for classifying Steiner triple systems is order 21. A Steiner triple system of order 21, an STS\((21)\), can have subsystems of orders 7 and 9, and it is known that there are 12,661,527,336 isomorphism classes of STS\((21)\)s with sub-STS\((9)\)s. Here, the classification of STS\((21)\)s with subsystems is completed by settling the case of STS\((21)\)s with sub-STS\((7)\)s. There are 116,635,963,205,551 isomorphism classes of such systems. An estimation of the number of isomorphism classes of STS\((21)\)s is given.

2020 Mathematics Subject Classification.   05B07

Key words and phrases.   Classification, Steiner triple system, subsystem

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https://doi.org/10.3336/gm.58.2.06

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