postEfficient mapping between index and permutation for very large n

I am exploring methods to compute a specific permutation from its index (ranking/unranking) without generating all permutations.

My focus is on very large values of n (e.g., up to 1000), where full enumeration is infeasible.

What are the most efficient known approaches or data structures for this problem?

Are there known limitations or practical implementations for such large n?