Generating all permutations by context-free grammars in Chomsky normal form

Let $L_n$ be the finite language of all $n!$ strings that are permutations of $n$ different symbols ($n\geq1$). We consider context-free grammars $G_n$ in Chomsky normal form that generate $L_n$. In particular we study a few families $\{G_n\}_{n\geq1}$, satisfying $L(G_n)=L_n$ for $n\geq1$, with respect to their descriptional complexity, i.e., we determine the number of nonterminal symbols and the number of production rules of $G_n$ as function of $n$.