Random Starter

Hey, I've a question about Random Starters option in the Randomizer menu, I've been wanting to start the game with a Feebas because of how terrible it is to get one normally in base Emerald, so I have been trying to force one to appear in the starter option by choosing the following settings:

​

Starter Randomizer

One type only: Water

​

But even after a few hours of attempts, they haven't appeared yet, so I was wondering if they are not in the eligible starter pool or if I'm doing something wrong.