If you live in a 2-d neighborhood the "four color theorem" proves you only need four codes to not share a code with a neighbor, assuming perfect information.

The wikipedia article for the four color theorm discusses higher dimensional life like being in a 3-d apartment building. If you live in a Klein bottle you got other problems beyond ceiling fans.

It's 16 possible fan identities for the range of a single remote. That should be enough for anybody.

It doesn't matter if two houses have the same identity as long as the remote in one doesn't reach the fan in the other.