Kirkman triple systems with subsystems

Dataset

Description

The files contain Kirkman Triple Systems classified in the study "J. I. Kokkala, P. R. J. Östergård, Kirkman triple systems with subsystems".

The file nonisom-stsk.txt contains equivalence class representatives of all KTS(21) that contain an STS(k) subsystem.

The file nonisom-ntauto.txt contains equivalence class representatives of all KTS(21) for which the underlying STS(21) has notrivial automorphisms. Note that this contains also some KTS(21) with a trivial automorphism group.

The file nonisom-tdkn.txt contains equivalence class representatives of all KTS(21) that contain a TD(k,n) subdesign.

Note that equivalence classes that fall into more than one of these categories occur in more than one file.

Each line in a file corresponds to one KTS(21) written as a (10,21,9)7 OE code. A line consists of the number of codewords (which is 21 for every code here) followed by a space-separated list of the codewords. The order of codewords in a line does not carry any significance.
Date made available2019

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