I need to simulate specific scenarios 1,000 times (to get the mean of an estimated value). Additionally, various sample sizes need to be specified.

I am recently reading the book by Testing Statistical Hypotheses (fourth edition) by Lehmann and Romano. At the page 565, theorem 12.2.2, there is a famous coupling construction popularly known as Hajek Coupling, where sum of SRSWOR (simple random sampling with replacement) indicator coupled with the sum of independent
Bernoulli indictor in a claver way. This method. was first describe in the paper of Hajek (1961).

I am building a simulation in R using the simmer package.