On the Construction of Triples of Diagonal Latin Squares of Order 10

We provide a triple of diagonal Latin squares of order 10 that is the closest to being a triple of mutually orthogonal diagonal Latin squares found so far. It was obtained by constructing all orthogonal mates for diagonal Latin squares generated according to a specific scheme. We also show that a triple of mutually orthogonal diagonal Latin squares of order 10 cannot be constructed based on diagonal Latin squares from specific families.