The most uniform sampling mesh in the unit square

Formal definition

• ContainerThe unit square, with (0, 0) at the lower-left corner and (1, 1) at the upper-right
• SubmissionExactly n points, each coordinate a decimal with at most nine places; no two points may coincide
• Covering radiush(P) is the distance from the worst-covered location in the square to its nearest submitted point$$h\left(P\right)=\underset{x\in {\left[0,1\right]}^2}{\max }\underset{1\le i\le n}{\min }\Vert x-p_i\Vert$$
• Separationδ(P) is the distance between the closest pair of submitted points$$\delta \left(P\right)=\underset{1\le i<j\le n}{\min }\Vert p_i-p_j\Vert$$
• ScoreM(P) penalizes both large holes and close pairs; internally M(P)² = 4h(P)²/δ(P)² is computed exactly, then rounded upward at 10⁻¹⁵$$M\left(P\right)=\frac{2h\left(P\right)}{\delta \left(P\right)}$$
• ObjectiveMake M(P) as small as possible over all legal point sets P$$\underset{P}{\min }M\left(P\right)$$