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The p discrepancy suffers from the curse of dimensionality for all finite p > 1.

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DREW01 - Multivariate approximation, discretization, and sampling recovery

The behavior of the inverse of the p discrepancy is known for more than 20 years for p = infinity (no curse) and for p = 2 (curse). Together with Fritz Pillichshammer (Linz) we now proved that the curse holds for all finite p > 1.  Only the case p = 1 is still open; our techniques do not work for p = 1.

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