In this paper, respectively 8, 10 and 9 mutually orthogonal Latin squares (MOLS) of sizes \(n=54\) , 96 and 108 are obtained (previously, only 5, 9 and 8 MOLS were respectively known for these values). The cases \(n=54\) and 96 are obtained by constructing separable permutation codes consisting of \(8 \times 54\) and \(10 \times 96\) codewords, respectively; in addition, these codes respectively have lengths 54, 96 and minimum distances 53, 95. This construction method was used in an earlier paper to obtain 6, 10 and 8 MOLS of sizes \(n=35\) , 54 and 63, respectively. The case \(n=108\) is obtained by constructing a (108, 10, 1) difference matrix. Also, a previous error when constructing 6 MOLS of size \(n=45\) is corrected.
