A Latin square transversal is a set of 
cells of an order-
Latin square containing exactly
one cell from each row, exactly one from each column, and exactly one of each symbol.
A duplex instead selects exactly two cells from each row, column, and symbol class
(Wanless 2002).
For the Latin square given by the addition table of 
,
Davis et al. (2026) enumerated 935373426152330923868160 transversals. For
,
Davis et al. (2026) enumerated 7112932178789358720 duplexes. Here 
is the direct sum of 
copies of the cyclic group of order 2.
