So, I assume that if you put 100 people on a spaceship and sent them to wherever, they’d get very inbred in a few generations. How many people would you need for this to not happen, accounting for the fact that there will eventually be people who are infertile or die before having children?
The obvious solution here is to include frozen gametes in the ship’s cargo to increase the diversity of the population. It would be culturally easiest with frozen sperm but if necessary you could include eggs as well, provided people are willing to be surrogate mothers.