Generalized Halton point set in 4 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.
| Dimensions | Number of Points | Star Discrepancy |
|---|---|---|
| 4 | 125 | 0.05609 |
| 625 | 0.01905 |
Point set obtained when searching for the minimal number of points required in 4 dimensions to have a star discrepancy < 0.0136.
| Dimensions | Number of Points | Star Discrepancy |
|---|---|---|
| 4 | 1048 | 0.01354 |
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