Generalized Halton point set in 7 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 of point sets with fixed number of points. 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 |
|---|---|---|
| 7 | 30 | 0.21349 |
| 40 | 0.18683 | |
| 49 | 0.16410 | |
| 50 | 0.16366 | |
| 60 | 0.14486 | |
| 65 | 0.13613 | |
| 70 | 0.13326 | |
| 80 | 0.12017 | |
| 90 | 0.11494 | |
| 100 | 0.10917 | |
| 110 | 0.10256 | |
| 120 | 0.09497 | |
| 130 | 0.09069 | |
| 140 | 0.08822 | |
| 145 | 0.08640 | |
| 150 | 0.08202 | |
| 160 | 0.08327 | |
| 170 | 0.08190 | |
| 180 | 0.07976 | |
| 190 | 0.07541 | |
| 200 | 0.07198 | |
| 210 | 0.06909 | |
| 220 | 0.06776 | |
| 230 | 0.06748 | |
| 240 | 0.06458 | |
| 250 | 0.06380 | |
| 343 | 0.05192 | |
| 2401 | 0.01518 |
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.
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