Determine the general No-Three-In-Line number

Determine the maximum number of points that can be selected from an n×n square lattice so that no three selected points are collinear, for general n.

Background

The paper recalls the classical No-Three-In-Line problem, which asks for the largest subset of the n×n grid containing no three collinear points. Although the universal upper bound is 2n and this bound is attained for several small values of n, the exact answer for arbitrary n remains unresolved.

References

However, it is still an open problem to determine the answer for general $n$.

— Settling the no-$(k+1)$-in-line problem when $k$ is not small  (2502.00176 - Kovács et al., 31 Jan 2025) in Section 1, Introduction