# Is there a space-filling curve with constant-time indexing?

The Hilbert curve and other space-filling curves I've read about seem to have mapping operations from 1-D index to N-dimensional coordinates that are efficient, but amount to a log-ish tree search IIUC.

Are there any space-filling curves that have constant-time conversion from 1-D to N-D space (maybe relying on constant time integer arithmetic)? Is this an impossible requirement?