Minimum star discrepancy in the unit square · n = 47
Also known asstar discrepancyminimum star discrepancylow-discrepancy point set
Place n points in the unit square [0, 1]². For every origin-anchored half-open rectangle [0, u) × [0, v), compare the fraction of points inside the box with its area uv, and minimize the supremum discrepancy D* over all such rectangles.
Instancen = 47
ObjectiveMinimize the worst gap D*
Record comparison
the worst gap D* · Lower is better| Record | Value / interval | Author / holder | Source |
|---|---|---|---|
| External best known | — | — | No reference listed |
| Site record | 0.028368794743443 | 邱仲普 | Record details ↓ |
Formal definition
- ContainerThe unit square [0, 1]², with lower-left corner at (0, 0) and upper-right corner at (1, 1)
- SubmissionExactly n distinct points, each coordinate written as a decimal string with at most nine decimal places
- RectanglesTest rectangles are half-open boxes [0, u) × [0, v) with (u, v) ∈ [0, 1]²; points on the top or right boundary count as outside
- Star discrepancyThe indicator 𝟙 is 1 when the point lies in [0, u) × [0, v) and 0 otherwise; D*(P) is the supremum absolute difference between the point fraction and the area uv
- ObjectiveMinimize D*(P) over all valid point sets P. The verifier evaluates the open and closed one-sided limits on the grid induced by the submitted coordinates and compares exact integers
