Obtaining O( N - 2+∈ ) Convergence for Lattice Quadrature Rules

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Fast construction of good lattice rules (2007, methodology): “From the analysis by Hickernell [45] it follows that the discrepancy for the smooth periodized function space is better, but the variation in that space is worse.”
Digital Nets and Sequences: Discrepancy Theory and Quasi-Monte Carlo Integration (2010, methodology): “The topic of improved rates of convergence was further developed first in [101] for lattice rules, and in [27] for polynomial lattice rules, using a random shift and the tent transformation.”
Collider physics at the precision frontier (2020, background): “ur0(1 u)r1 R 1 0 dttr0(1 t)r1 = (r 0 + r 1 + 1) r 0 + r 1 r 0 ur0(1 u)r1; (76) The weight parameters r 0;r 1 are usually chosen to be equal. Another useful transformation is the baker’s transform [906] (also called \tent transform"), given by ˚(u) = 1 2u 1 = 8 < : 2u if u1 2; 2 2u if u>”
Monte Carlo and Quasi-Monte Carlo Sampling (2009, background): “One such example is the baker transformation of Hickernell [167], where each coordinate ui,j is replaced by 2ui,j if ui,j < 0.”
Comparison of Methods for the Computation of Multivariate t Probabilities (2002, methodology): “If the dimensionof v is m or m ¡ 1, we use good lattice point sets (see Sloan and Joe 1994; Hickernell 1998) for the required quasirandom point sets.”