We report the results of a computer investigation of sets of mutually orthogonal latin squares (MOLS) of small order. For n 9 we 1. Determine the number of orthogonal mates for each species of latin square of order n. 2. 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. 3. 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.
In the paper REF the enumeration of mutually orthogonal Latin squares of order 9 was performed.
Enumeration of MOLS of small order
Mathematics of Computation 85, 2016, 799-824
Mathematics Computer Science