Because multiplying by swap permutation takes short computing time and every new generated permutation requires only one such swap multiplication, this generation procedure is quite efficient. Moreover as there is a simple formula, having the last permutation in each can save even more time to go directly to a permutation with certain index in fewer steps than expected as it can be done in blocks of subgroups rather than swap by swap.
Because multiplying by swap permutation takes short computing time and every new generated permutation requires only one such swap multiplication this generation procedure is quite efficient. Moreover as there is a simple formula, having the last permutation, i.n each can save even more time to go directly to a permutation with certain index in fewer steps than expected as it can b.e done in blocks of subgroups rather than swap by swap.