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Date: 6-2-2016
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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.
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