A short disproof of Euler's conjecture based on quasi-difference matrices and difference matrices

In this note, two classes of quasi-difference matrices, (2n+2,4;1,1;n)-QDM and (4n+1,4;1,1;2n−1)-QDM, are constructed. Combining the known results of quasi-difference matrices and difference matrices, a new short disproof of Euler's conjecture on mutually orthogonal Latin squares is given.