DR12 - Generalized Halton Sequence
An evolutionary optimized generalized halton sequence. The optimization has been made by minimizing the modified L2 discrepancy criterion of the 2500 first points of the sequence. The process optimized one dimension at a time starting with a sequence in one dimension and adding one dimension to the sequence at a time. When optimizing the sth dimension, the first s-1th were kept the same. See De Rainville et al. 2012 for more details.
The modified L2 discrepancy of the first 2500 points in 20, 50, and 100 dimensions is respectively 0.4166, 172851, and 0.2604e14.
The L2-star discrepancy of the first 2500 points in 20, 50, and 100 dimensions is respectively 0.3550e-9, 2.359e-21, and 0.7772e-45.
The maximum dimensinality of the sequence is 100 dimensions.
The configuration vectors have been stacked over the optimization meaning that the x first coordinates of the nth point will be the same for two sequences in x and y dimensions with x < y.
The permutation vectors are put in a list. For example, the first five dimensions are configured with the first five permutations from the list.
F.-M. De Rainville, C. Gagné, O. Teytaud, and D. Laurendeau. Evolutionary optimization of low-discrepancy sequences. ACM Trans. Model. Comput. Simul., 22(2):9:1–9:25, 2012.