An exact formula for the L2 discrepancy of the symmetrized Hammersley point set

The process of symmetrization is often used to construct point sets with low Lp discrepancy. In the current work we apply this method to the shifted Hammersley point set. It is known that for every shift this symmetrized point set achieves an Lp discrepancy of order O(logN/N) for p∈[1,∞), which is best possible in the sense of results by Roth, Schmidt and Halász. In this paper we present an exact formula for the L2 discrepancy of the symmetrized Hammersley point set, which shows in particular that it is independent of the choice for the shift.