  We report the results of a computer investigation of sets of mutually
orthogonal latin squares (MOLS) of small order. For $n\le9$ 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.
