I'm creating a necromancer wizard player character and searching for the most optimal amount of undead to control. I searched for the lore of the monsters, and found that Ghasts tend to be leaders in packs of ghouls. But I couldn't find how a Ghast does that, or how many can it can maintain in order.

So that makes me wonder. Can a controlled ghast be the boss of an uncontrolled pack of ghouls? And if he can, how many could it command?

That could significantly boost the amount of undead my necromancer could control by indirect means:

The idea I have is to create ghouls using my 6th level spell slot, and maintain the superior slots for a ghast, who will introduce the newcomers to the pack, so when the next day comes, they already are in a group controlled be the more powerful undead, who will in turn be controlled by me.

You are talking about NPC interactions

When it comes to a ghast's command of ghouls, it isn't some magical effect. It is simply the ghast's greater power and "cunning"...

inspir[ing] a pack of ghouls to follow its commands.

This is similar to how a powerful bugbear might inspire a collection of lowly goblins. Since it is simply a matter of character interaction, it will be ultimately up to the GM how this works.

Ghouls are not particularly intelligent creatures, so if they are already in league with a ghast they may become tag-alongs as long as you keep them well-fed. Whether or not your ghast can command a new group of ghouls will largely depend on what exactly motivates the ghouls in a particular situation.

This sort of thing isn't specified.

The "ghasts as leaders of ghoul packs" thing is a matter of monster social groups. That's meant to be handled by the DM. Monster descriptions in the Monster Manual and other sources are only intended to provide suggestions, guidelines, and inspiration. The expectation is that all of the pack members will be acting as monsters, and therefore that explicit rules about how they interact aren't necessary, or even particularly useful.

You might get it to work, but it probably won't get you the kind of control you actually need.

Control Undead says that the ghast in question will follow your commands to the best of its ability. That's great! That means that you can pretty easily get it to lead the pack for you, to the best of its ability. The issue here, though, is that the ghouls aren't controlled. They're just a pack. They're going to act like ghouls in a pack, and by default, they're chaotic evil. So, you can get the ghast to make the ghoul pack do ghoul pack things - like, say, go off and terrorize a village or something. They're int 7, so you might be able to intimidate them into doing the same yourself, if you had a good enough intimidate score. (They speak Common, just like everybody else). You're not going to get them to do things like guard treasure indefinitely, though, or not go scuttling off to eat someone if they see a chance at some easy meat. They're still chaotic evil. The control their packleader has over them is... not likely to be amazing.

Ghasts have no power over ghouls

A ghast has no power to control other ghouls or any other lesser undead. So controlling it gives you nothing really. Unless you manage to hide your control from the rest of the pack, you will only control it.

Now, you may be able to coerce the rest of the pack into obedience through fear of your magical power. Such control is limited at best and likely to end poorly the first time you go to sleep, so be very careful with it.

You may bribe them into working for/with you, spying or performing tasks that does not endanger them. Again, such "control" will only last as long as you can pay them with something they want.

Other creatures may create a "chain of charm" but not ghasts and ghouls.