DDR13 - Generalized Halton Point Set - 10 dimensions

Generalized Halton point set in 10 dimensions optimized over the star discrepancy by an evolutionary algorithm as described in Doerr and De Rainville 2013.


Point sets obtained when minimizing the star discrepancy. Italic values are approximated by running 50 times the TA algorithm described in Gnewuch et al. 2012 and available here, with 10 000 iterations each.

Dimensions Number of Points Star Discrepancy
10 121 0.13344
1331 0.03251

Point set when searching for the minimal number of points required in 10 dimensions to have a star discrepancy < 0.0575.

Dimensions Number of Points Star Discrepancy
10 574 0.05744


The permutation vectors in the JSON file are values of a dictionary where the key is the number of points (as string). Points sets should be read row major; an entire row is a point and each column is one dimension for a point.

Cite As

C. Doerr, and F.-M. De Rainville. Constructing Low Star Discrepancy Point Sets with Genetic Algorithms, In Proceedings of the Genetic and Evolutionary Computation Conference, 2013.
ArXiv Version


M. Gnewuch, M. Wahlström, and C. Winzen. A New Randomized Algorithm to Approximate the Star Discrepancy Based on Threshold Accepting. SIAM Journal on Numerical Analysis, 50:781-807, 2012.
Official Version
MPI Dep. Version

Quasi-random Sequences Repository © 2021
Powered by GetSimple