Genius Breeding Act: Averted, despite the tremendous respect for intelligence – as you might expect from the civilization that considers Arranged Marriages an unpleasant subclass of slavery. (Which, as I said back then, doesn’t mean that friends and relatives aren’t happy to engage in generous quantities of Shipper on Deck…)
…actually, more inverted, in a sense. The Reproductive Statutes do do the opposite, since while fully recognizing the rights, etc., of those with hereditary disabilities, since ethics is time-directional, that does not extend to deliberately or negligently creating more of them, respecting the right of the potential sophont to be well-created. And for a sufficiently advanced society, “hereditary disabilities” includes “functional amentia” to a degree that goes a long way farther than anything anyone in our history would have classed as even mild intellectual disability or other related conditions.
So if your genes aren’t up to scratch in this area, no reproduction for you! That’d be felony dysgenesis.
Population Control: Averted. This is the thing the Empire’s Reproductive Statutes don’t do. (They exist mostly to prevent violating the rights of about-to-be sophonts by creating them below the acceptable minimums for their species; this exercise in eugenics primarily means “no hereditary diseases or defects”, but does go so far as to define that as including things like “being stupid or unbearably ugly”, and includes high-p probabilities of your parents rendering you defective in non-genetic ways. On the other hand, they don’t function as even stealth population control, because the odds are that if your genes are too out of whack for the genetic designers to wrangle into shape somehow, you didn’t live long enough to think about reproducing anyway.
They also prohibit having children which you can’t support – because reproduction is not a right if it means either harming the child or stealing from the public purse – which is mostly not a consideration in the splendidly wealthy modern Empire, but has been a bit more controversial in historical times.)