Consult the crystal ball.

I have one, but I don’t want to look at it. So, random mode is the best. The percentages are the same as the prefixes. There’s no connection anywhere here

A waste of time. Trust me, I’ve done tons of tests and confirmed that random can be fast (done this on low 44-bit ranges), but it can scan 4 times the entire range without a single result. That means duplication, and avoiding it completely is nearly impossible. Totally a waste of time.
You can avoid duplication completely with a Feistel network.