Deterministic dynamic dictionary on a small universe
If randomness is allowed, you can get space $B + o(B)$ and time $O(1)$ (worst-case, with high probability), where $B$ is $\lg {U \choose n}$, which is the lower bound on how much space you need using any representation: Arbitman et al., " Backyard Cuckoo Hashing: Constant Worst-Case Operations with a Succinct Representation".

For deterministic dictionaries, the best known bounds are discussed in Thorup's "Mihai Pǎtraşcu: Obituary and Open Problems"