A power improvement in the Heilbronn triangle lower bound

There are absolute constants $\eta,c_1\gt 0$ such that, for every sufficiently large integer n, one can choose n points in the unit square so that every triangle they determine has area at least $c_1n^{-2+\eta}$. Thus the almost n−2 upper-bound formulation of Heilbronn's triangle problem is false. The exponent η is fixed but extremely small.