  In this paper we provide results on using integer programming (IP) and
constraint programming (CP) to search for sets of mutually orthogonal latin
squares (MOLS). Both programming paradigms have previously successfully been
used to search for MOLS, but solvers for IP and CP solvers have significantly
improved in recent years and data on how modern IP and CP solvers perform on
the MOLS problem is lacking. Using state-of-the-art solvers as black boxes we
were able to quickly find pairs of MOLS (or prove their nonexistence) in all
orders up to ten. Moreover, we improve the effectiveness of the solvers by
formulating an extended symmetry breaking method as well as an improvement to
the straightforward CP encoding. We also analyze the effectiveness of using CP
and IP solvers to search for triples of MOLS, compare our timings to those
which have been previously published, and estimate the running time of using
this approach to resolve the longstanding open problem of determining the
existence of a triple of MOLS of order ten.
