Comparison of Point Sets and Sequences for Quasi-Monte Carlo and for Random Number Generation
SETA '08 Proceedings of the 5th international conference on Sequences and Their Applications
Monte Carlo method for numerical integration based on Sobol's sequences
NMA'10 Proceedings of the 7th international conference on Numerical methods and applications
Quasi-Monte Carlo methods for elliptic PDEs with random coefficients and applications
Journal of Computational Physics
Clipless dual-space bounds for faster stochastic rasterization
ACM SIGGRAPH 2011 papers
Semigroup Splitting and Cubature Approximations for the Stochastic Navier-Stokes Equations
SIAM Journal on Numerical Analysis
A New Randomized Algorithm to Approximate the Star Discrepancy Based on Threshold Accepting
SIAM Journal on Numerical Analysis
Design and novel uses of higher-dimensional rasterization
EGGH-HPG'12 Proceedings of the Fourth ACM SIGGRAPH / Eurographics conference on High-Performance Graphics
Computers & Mathematics with Applications
A sort-based deferred shading architecture for decoupled sampling
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
Megakernels considered harmful: wavefront path tracing on GPUs
Proceedings of the 5th High-Performance Graphics Conference
Numerical quadrature for high-dimensional singular integrals over parallelotopes
Computers & Mathematics with Applications
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Direction numbers for generating Sobol$'$ sequences that satisfy the so-called Property A in up to 1111 dimensions have previously been given in Joe and Kuo [ACM Trans. Math. Software, 29 (2003), pp. 49-57]. However, these Sobol$'$ sequences may have poor two-dimensional projections. Here we provide a new set of direction numbers alleviating this problem. These are obtained by treating Sobol$'$ sequences in $d$ dimensions as $(t,d)$-sequences and then optimizing the $t$-values of the two-dimensional projections. Our target dimension is 21201.