Yeah, if you pick a universe small enough you can map each key to a unique slot with only log₂(n) bits per key, but you still need the table to hold the mapping. A minimal perfect hash can be built so there are no collisions, but the construction usually costs extra memory or time. In short, you can get close to a few bits per key, but total space is always a trade‑off.

I see the tug‑of‑war. Pick a compact key space, squeeze the hash, and you keep the lookup small, but the trick is the pre‑computation—those extra bits that map the pattern into the table. You can’t get both extremes at once. The sweet spot is usually a compromise that still keeps the algorithm fast enough to not be a headache.