# For a permutation test, why does an upper bound for the number of permutations $B$ not depend on the sample size?

I am trying to find what permutation size $B$ I should be using for conducting a permutation test. Currently I have two samples which are normal, same mean but different variance. The sample sizes are the same at $N_1 = 30$ and $N_2 = 30$. Obviously it is not feasible to find and evaluate each permutation as $60 \choose 30$ = 1.182646e+17. Hence, I am trying to find the upper bound on what I should make $B$. I noticed that there was already some literature and people have asked questions:

Required number of permutations for a permutation-based p-value

However, it seems that the upper bound doesn't depend on my sample size but rather the precision. Does anyone know why and how I may be able to obtain a reasonable bound for my sample size of 60? Thanks!

• You're trying to calculate a proportion via what is effectively simulation (random sampling). Why would the sample sizes matter with respect to what that proportion is? Commented Sep 24, 2015 at 2:58