de Mathématiques de Luminy
Faure Henri, Pillichshammer Friedrich.
Lp discrepancy of generalized two-dimensional Hammersley point sets
We determine the Lp discrepancy of the two-dimensional Hammersley point set in base b. These formulas show that the Lp discrepancy of the Hammersley point set is not of best possible order with respect to the general (best possible) lower bound on Lp discrepancies due to Roth and Schmidt. To overcome this disadvantage we introduce permutations in the construction of the Hammersley point set and show that there always exist permutations such that the Lp discrepancy of the generalized Hammersley point set is of best possible order. For the L2 discrepancy such permutations are given explicitly.