An algebraic derivative associated to the operator $D^δ$

V. Almeida; N. Castro; J. Rodríguez

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We give an exact formula for the $L_{2}$ discrepancy of a class of generalized two-dimensional Hammersley point sets in base $b$ , namely generalized Zaremba point sets. These point sets are digitally shifted Hammersley point sets with an arbitrary number of different digital shifts in base $b$ . The Zaremba point set introduced by White in 1975 is the special case where the $b$ shifts are taken repeatedly in sequential order, hence needing at least $b^{b}$ points to obtain the optimal order of $L_{2}$ discrepancy....