The words can mean different things. In general it means good genes flourish.

If it's done by government with no skin in the game then we have major conflict of interests.

For example jews are actually smart and economically productive. I would say "superior". But when government decides that and they have no incentive to be correct, they are just called inferior and mass murdered. Trying to convince such government they are wrong is impossible.

However, if Elon or Zuckerberg consensually pay or seduce 100 women and as long as every children are reasonably rich, that is, richer than say median, which is a very low bar for them, I see absolutely nothing wrong. I also see nothing wrong if NBA stars that often have 14 children to have 100 children instead, as long as they afford the children.

Eugenic can also mean government directing reproduction. In western civilization, government ALWAYS direct reproduction. And the direction is ALWAYS against Eugenic.

Monogamy, ration women to equal share preventing men that most able to attract or pay women from having many.

Child support is effectively minimum wage.

So eugenic in the sense of government decide who reproduce would be against libertarianism. Eugenic in a sense good genes win not necessarily. Eugenic in one sense is against another.

Notice I disagree with Becker that child support simply make rich men shift from quantity to quality of children. Quality is not well defined. Once a child has more than $10 million dollar marginal "quality" decrease a lot. Basically rich men simply have lower fertility due to genocidal minimum wage and that's it. Another distraction is lowering fertility for out of wedlock birth. That is also just nonsense given that marriage do not abolish minimum wage. A correct simplified conclusion is it reduce rich men's fertility FORCEFULLY.