The tent transformation can improve the convergence rate of quasi-Monte Carlo algorithms using digital nets

In this paper we investigate multivariate integration in reproducing kernel Sobolev spaces for which the second partial derivatives are square integrable. As quadrature points for our quasi-Monte Carlo algorithm we use digital (t,m, s)-nets over Z2 which are randomly digitally shifted and then folded using the tent transformation. For this QMC algorithm we show that the root mean square worst-case error converges with order 2m(−2+ε) for any ε > 0, where 2m is the number of points. A similar result for lattice rules has previously been shown by Hickernell.