Conjectured improved upper bound for the Heilbronn triangle problem

Let $\Delta_{\mathrm H}(n)$ denote the largest possible minimum area of a triangle determined by $n$ points in the unit square. Improved Heilbronn bound conjecture. There exists an absolute constant $c>0$ such that

$$\Delta_{\mathrm H}(n)\lesssim n^{-7/6-c}.$$

This would improve the known upper bound $\Delta_{\mathrm H}(n)\le n^{-7/6+o(1)}$ and reflects the expectation that the sharp $2/3$ exponent for the minimal point–line distance problem does not settle the Heilbronn triangle problem.