Efficient algorithm to find the nth number in a base-k numeral system with only different digits
Your problem is known as unranking permutations in lexicographic order.  Bonet, Efficient Algorithms to Rank and Unrank Permutations
in Lexicographic Order describes efficient algorithms, and contains some pointers to the literature.

As described in the paper, more efficient algorithms are possible if you don't insist on lexicographic order.