Implementing the MOLS Table for n Up to 500

Latin squares are an essential tool in the construction of combinatorial designs. Optimal solutions for problems such as scheduling problems and permutation arrays for powerline communication rely on the ability to construct sets of mutually orthogonal Latin squares (MOLS) that are as large as possible. Although constructions of suitable sets are known, they are scattered among a wide variety of sources, and can be both difficult to understand and contain errors. We describe our experience implementing the largest known sets of MOLS of order n, for n up to 500. We give a source for each construction, provide additional hints for the difficult cases, and correct some errors along the way. We also give constructions for new sets of MOLS of order n, where n is 486, 567, 622, 635, 754, 756, 764, 766, 774, 778, 802, 810, 822, 826, 894, 906, 916, 920 or 936.