Fractional general position number of grids

Determine the fractional general position number of Cartesian grid graphs.

Background

The fractional general position number is formulated as a linear program. For square grids, the survey gives lower and upper bounds that are asymptotically close, but exact values are known only for small orders, leaving the grid problem unresolved.

References

Exact values are only known for $n \leq 7$; however, by making use of the symmetry of the grid, Erskine and Tuite have shown that the lower bound is best possible for $n \leq 10$.

— The General Position Problem: A Survey  (2501.19385 - V. et al., 31 Jan 2025) in Section 7, subsection “Fractional position problems”