Institut
de Mathématiques de Luminy

Abstract 2008-07 |

**Faure** Henri, **Pillichshammer** Friedrich.

*L _{p}* discrepancy of generalized two-dimensional Hammersley point sets

We determine the b. These formulas show that the L discrepancy of the Hammersley point set is not of best possible order with respect to the general (best possible) lower bound on _{p}L 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 _{p}L discrepancy of the generalized Hammersley point set is of best possible order. For the _{p}L discrepancy such permutations are given explicitly. _{2}AMS subject classification: 11K06, 11K38. Key words: L discrepancy, Hammersley point set. _{p} |