Yes you are correct it’s the first three (say) bytes (8 bits each)so 2^24. I will give links to the detailed design docs, it’s my anathema providing info people can understand and not too much. We can give the whole design in detail, but then folk don’t want that much detail. Maybe best to say in overview collisions are tiny 
Even 2^15 is still tiny (hex char set so larger than this, I can get the exact figures but lets keep that to the detailed design parts which will get published (they are already).
If we say there are about the same amount of grains of sand on the planet as there can be unique ID’s then for most this will be enough. I Think you are right if we go into detail it will be around 2^18-20 depending on char et for collision avoidance and 2^80(ish) for full id’s.