- Latin squares without transversals
- Confirmed bachelor latin squares (i.e. ones with at least
one entry not in a transversal). Each file is in increasing order of number
of transversal-free entries.
- Latin squares with the fewest number of transversals. For
even orders we know of latin squares without transversals (see above),
so this is really only of interest for odd orders.
- Order 3 (3 transversals)
- Order 5 (3 transversals)
- Order 7 (3 transversals)
- Order 9 (68 transversals)
- Order 11 (778 transversals -- may not be the least possible, but has the fewest among the many squares I've checked)

- Latin squares with the fewest number of
*disjoint*transversals. For even orders we know of latin squares without transversals (see above), so this is really only of interest for odd orders.- Order 5 (all transversals intersect)
- Order 7 (all transversals intersect)
- Order 9 (at most 3 disjoint transversals)

- Latin squares with the largest number of transversals.
- Order 3 (3 transversals)
- Order 4 (8 transversals)
- Order 5 (15 transversals)
- Order 6 (32 transversals)
- Order 7 (133 transversals)
- Order 8 (384 transversals)
- Order 9 (2241 transversals)
- Order 10 (5504 transversals -- provisional winner)
- Order 11 (37851 transversals -- provisional winner)
- Order 12 (198144 transversals -- provisional winner)
- Order 13 (1030367 transversals -- provisional winner)
- Order 14 (3477504 transversals -- provisional winner)
- Order 15 (36362925 transversals -- provisional winner)
- Order 16 (244744192 transversals -- provisional winner)
- Order 17 (1606008513 transversals -- provisional winner)
- Order 18 (6434611200 transversals -- provisional winner*)
- Order 19 (87656896891 transversals -- provisional winner)
- Order 20 (697292390400 transversals -- provisional winner)

_{9}×Z_{2}. In the first square the 4 turned entries are consecutive. In the second there is a gap of one place before the 4th turned entry. - Latin squares in which every set of disjoint transversals extends
to a 1-partition (files are ordered by decreasing number of transversals, and orthogonal mates).
- Latin squares that contain a transversal that intersects every
other transversal. Files are ordered in increasing order of the
size of the largest set of disjoint transversals.

If you want to know what format these files are in, it is my usual latin squares format.