Most Efficient Way to List All $n$-bit Permutations
Since $n$ is known from the start, you know that there are exactly $2^n!$ possible lists.  Calculate the index of your list in a lexical ordering of all permutations, and then write that number using $\lceil log_2(2^n!)\rceil$ bits.

In practice, you can come arbitrarily close to this bound using arithmetic encoding, without having to manipulate very large integers.