L. Plaskota

The exponent of discrepancy of sparse grids is at least $2.1933$

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Abstract.   We study bounds on the exponents of sparse grids for $L_2$-discrepancy and average case $d$-dimensional integration with respect to the Wiener sheet measure. Our main result is that the minimal exponent of sparse grids is for these problems bounded from below by $2.1933$. This shows that sparse grids provide a rather poor exponent since, due to Wasilkowski and Wozniakowski, the minimal exponent of L_2-discrepancy of arbitrary point sets is at most $1.4778$. The proof of the latter is however non-constructive. The best known constructive upper bound is still obtained by a particular sparse grid and equal to $2.4526...$

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