A lower bound on permutation codes of distance $n-1$

A classical recursive construction for mutually orthogonal latin squares (MOLS) is shown to hold more generally for a class of permutation codes of length $n$ and minimum distance $n-1$. When such codes of length $p+1$ are included as ingredients, we obtain a general lower bound $M(n,n-1) \ge n^{1.079}$ for large $n$, gaining a small improvement on the guarantee given from MOLS.