• maps d-dimensional vectors onto points on a line
  i.e. [0,1)^d [0,1)

• mapping is one-to-one and defines an order on [0,1)^d

• inverse mapping is continuous

Points within a small region of the curve are likely to have been mapped from vectors that are close in d-space.

We generate multiple C_is by applying:

• permutations over vector elements

• translations of individual elements