Algorithm

Pure mathematics

Discrete mathematics

Statistics

Sobol sequence

Applied mathematics

Dimension (graph theory)

Set (abstract data type)

Computer science

Mathematics

Combinatorics

Monte Carlo method

Programming language

SIAM Journal on Scientific Computing

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.

Constructing Sobol Sequences with Better Two-Dimensional Projections