Geodesic
Average discrepancy for periodic integrands
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 8 (2005) no. 4, pp. 353-362.

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In the numerical integration of periodic integrands over the $s$-dimensional unit cube, various performance criteria such as $P_{\alpha}$ and $R$ have previously been used. In this paper, we use a criterion called $L_2$ discrepancy. An analogue of this quantity has previously been used to study the error in the case of non-periodic integrands. For this quantity we obtain expressions for the average in the case of number-theoretic and $2^s$ copy rules. The values of these averages are then compared for roughly the same number of points 
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M. V. Reddy. Average discrepancy for periodic integrands. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 8 (2005) no. 4, pp. 353-362. http://geodesic.mathdoc.fr/item/SJVM_2005_8_4_a7/

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