Your algorithm will never shuffle a deck of cards because randomly selecting a 64 digit means your N(logN) algorithm will need to generate on average the 2^63th or larger permutation. It’ll be several millennia for every deck shuffle. If you don’t believe me try to write it.
Also, I’m not really sure your nlog(n) algorithm claim is accurate - python’s itertools says that the time complexity to generate the Nth permutation is still N!. So for a 52 deck card on average you’re going to have to generate 2^88 permutations.
By comparison, shuffling is O(n) where your n is the number of items.
