The permutation test using the usual $F$-statistic from a randomized block experiment is considered under a randomization model. Alternative hypotheses assuming additive treatment effects are considered. It is shown that the critical value of the test statistic tends to a constant in probability as the number of blocks becomes large. The large-sample power of the test is calculated for a sequence of alternatives arising naturally from the randomization model.
"The Large-Sample Power of Permutation Tests for Randomization Models." Ann. Statist. 1 (2) 291 - 296, March, 1973. https://doi.org/10.1214/aos/1176342366