Sure but 2^n space complexity to get O(1) time complexity works for all n even infinite. Thats the end state of Blums speedup theorem in either direction and it doesn’t limit to any bounds. I just stating a limited of bounds above for the sake of giving understanding. Complexity theory doesn’t care that 2^n space complexity doesn’t work when n is infinite anymore than it cares that nlogn also doesn’t work when n is infinite. It’s not the point.

no it doesn't. making the table takes O(2^n) time

nah dude. i'll allow any finite size lookup table, but not an infinite one.