Kirkman triple systems with subsystems

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.