because the symmetric group on elements has size !, choosing a truly random permutation from the full symmetric group is infeasible for even moderately sized . because of this fact, there has been significant work on finding a family of permutations that is "min-wise independent" — a permutation family for which each element of the domain has equal probability of being the minimum under a randomly chosen . it has been established that a min-wise independent family of permutations is at least of size formula_68, and that this bound is tight.