Let's say an isolated colony is established in an ideal environment with the goal of growing the inhabited human population as quickly as possible. Health care is provided for them by managers, or those that own the colony, and is roughly up to twenty-first century standards with improvement on gene technology. Those in the colony are not allowed to develop technology beyond that used in the nineteenth century to quell any possibility of a successful uprise against their managers, but they are given the means to be self-sufficient. They can grow their own food, they are allowed to be educated enough to read and have a trade, and have laws enforced by their managers to kepp them 'in line'.
How long would it take for one hundred couples in the colony (one hundred men, one hundred women) - all of good genes, with no genetic diseases - to make one million descendants? That is, if Generation A had two hundred people in it and started having children at the age of sixteen (and were allowed to have as many children as possible), and every generation started having children at the same age (and are also allowed to have as many children as possible), how many generations would it take for a generation to be made up of one million individuals?
It is illegal to have sex outside of marriage, and marriages are preapproved by managers to ensure there are no genetic issues - rather, only couples with low chances producing sickly children are allowed to marry and reproduce with each other. Assuming they keep genetics records of every individual, and then get samples from all of their children to have their genetics as well so they have on record who the parents are, I assume inbreeding would still be an issue at some point. How long would it be before inbreeding became a problem? Could they hit the one million mark before that?