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L_2 discrepancy of symmetrized generalized Hammersley point sets in base b
[article]
2016
arXiv
pre-print
Two popular and often applied methods to obtain two-dimensional point sets with the optimal order of L_p discrepancy are digit scrambling and symmetrization. In this paper we combine these two techniques and symmetrize b-adic Hammersley point sets scrambled with arbitrary permutations. It is already known that these modifications indeed assure that the L_p discrepancy is of optimal order O(√(N)/N) for p∈ [1,∞) in contrast to the classical Hammersley point set. We prove an exact formula for the
arXiv:1511.04937v2
fatcat:52tlppko7reg3dog4moupfjtdy