It’s been a few years, but IIRC, in my six sigma/stats class, we were taught that n must be at least 10, or if you know the population, than n must be at least 10%.[pedant]
I'm going to go ahead and disagree on your sampling methodology. You can't choose n (sample size) until you have an idea of the mean variation within the sample and the mean variation between comparison groups. Then you need to calculate a sample size sufficient to find a difference 19 times out of 20.
[/pedant]
Sorry, my business runs on getting sample sizes right.
But in your line of work, I’m sure the standards are higher for obvious reasons.