Enumeration of MOLS of small order
We report the results of a computer investigation of sets of
mutually orthogonal latin squares (MOLS) of small order. For n≤9 we
- Determine the number of orthogonal mates for
each species of latin square of order n.
- Calculate the proportion of latin squares of order n that have
an orthogonal mate, and the expected number of mates when a square is
chosen uniformly at random.
- Classify all sets of MOLS of order n up to various different
notions of equivalence.
We also provide a triple of latin squares of order 10 that is the closest
to being a set of MOLS so far found.
Some
auxillary data is available for this paper.