A summary of the MTS(12)'s


KEY:
=====
|G| =   The automorphism group size of the corresponding designs.

Nd  =   The number of non-isomorphic orientable TTS(12) designs,
        which admit at least one MTS(12) design, by group size.

MTS =   The number of inequivalent Mendelsohn Triple Systems admitted
        by the underlying TTS(12) designs of the corresponding group size

Distinct = The number of distinct orientable TTS(12) designs.

|G|     Nd      MTS     Distinct
----    ----    -----   ---------
1536    1       3       311850
576     1       2       831600
432     1       7       1108800
192     3       4       7484400
144     1       4       3326400
128     2       5       7484400
72      2       6       13305600
64      2       6       14968800
54      1       1       8870400
48      6       12      59875200
36      1       2       13305600
32      9       15      134719200
24      7       15      139708800
18      2       3       53222400
16      24      40      718502400
12      15      38      598752000
9       1       1       53222400
8       77      173     4610390400
6       106     196     8462361600
4       482     867     57719692800
3       531     647     84783283200
2       11011   15003   2637143308800
1       4679953 4888643 2241704974924800

Totals: 4692239 4905693 2244499522961850

So there are 4,692,239 non-isomorphic, orientable, TTS(12) designs -
admitting at least one MTS(12).

Paul Denny (pden001@studpop.cs.auckland.ac.nz) has stored each of
these designs on disc, and says there are many interesting statistics
which can be calculated from them.