%0 Journal Article
%T $L_2$ discrepancy of linearly digit scrambled Zaremba point sets
%A Henri Faure
%A Friedrich Pillichshammer
%A Gottlieb Pirsic
%J Uniform Distribution Theory
%D 2011
%I Mathematical Institute of the Slovak Academy of Sciences
%X We give an exact formula for the $L_2$ discrepancyof a class of generalized two-dimensional Hammersley point sets in base $b$, namely generalized Zaremba point sets.For the construction of such point sets one needs sequences of permutations of the form $\pi_l(k)=\alpha k +l \pmod{b}$ for $k,l \in {0,\ldots,b-1}$. As a corollary we obtain a condition on these sequences which yields the best possible order of $L_2$ discrepancy of generalized Zaremba point sets in the sense of Roth's lower bound, with very small leading constants.
%K $L_2$ discrepancy
%K generalized Hammersley point set
%K linear digit scrambling
%U http://www.boku.ac.at/MATH/udt/vol06/no2/05%20FPP.pdf