  Commonly the direct construction and the description of mutually orthogonal
Latin squares (MOLS) makes use of difference or quasi-difference matrices. Now
there exists a correspondence between MOLS and separable permutation codes. We
like to present separable permutation codes of length $35$, $48$, $63$ and $96$
and minimum distance $34$, $47$, $62$ and $95$ consisting of $6 \times 35$, $10
\times 48$, $8 \times 63$ and $8 \times 96$ codewords respectively. Using the
correspondence this gives $6$ MOLS for $n=35$, $10$ MOLS for $n=48$, $8$ MOLS
for $n=63$ and $8$ MOLS for $n=96$. So $N(35) \ge 6$, $N(48) \ge 10$, $N(63)
\ge 8$ and $N(96) \ge 8$ holds which are new lower bounds for MOLS. The codes
will be given by generators of an appropriate subgroup $U$ of the isometry
group of the symmetric group $S_n$ and $U$-orbit representatives. This gives an
alternative uniform way to describe the MOLS where the data for the codes can
be used as input for computer algebra systems like MAGMA, GAP etc.
