Hammersley Point Set

The two-dimensional Hammersley point set of order  is defined by taking all numbers in the range from 0 to  and interpreting them as binary fractions. Calling these numbers , then the corresponding  are obtained by reversing the binary digits of . For example, the  for the Hammersley point set of order 2 are given by , , , and , or (0, 1/2, 1/4, 3/4). Reversing the bits then gives the second component, leading to the set of points (0, 0), (1/2, 1/4), (1/4, 1/2), and (3/4, 3/4).

The point set can be generalized by truncating  bits from each coordinate. The result is known as a binary -net, with  representing the dimension (in this case, ). Examples of these sets are illustrated above for , , and various degrees of truncation.