L_2 discrepancy of symmetrized generalized Hammersley point sets in base b [article]

Ralph Kritzinger, Lisa M. Kritzinger
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
more » ... _2 discrepancy of these point sets for special permutations. We also present the permutations which lead to the lowest L_2 discrepancy for every base b∈{2,...,27} by employing computer search algorithms.
arXiv:1511.04937v2 fatcat:52tlppko7reg3dog4moupfjtdy