McKay, Meynert, Myrvold (2006) (Small latin squares, quasigroups, and loops, DOI:10.1002/jcd.20105, author copy) computationally eliminate the possibility of set of 3 mutually orthogonal Latin squares of order 10, i.e., a 3-MOLS(10), where one of the Latin squares has a non-trivial autoparatopism group (i.e., it has some symmetry).
I'm unsure of what the current status for 3-MOLS(10) in which one is self-orthogonal (i.e., orthogonal to its transpose), and another is its transpose. It seems like this could be within the realm of computational feasibility.
Question: Has the existence of a 3-MOLS(10) containing a self-orthogonal Latin square and its transpose been eliminated?
