Nagata's numerical inequality for effective classes

Let $X$ be obtained by blowing up $r>9$ generic points of $\mathbb{P}^{2}$. Let $L$ be the pullback of a line and let $E_1,\ldots,E_r$ be the exceptional divisors. Let $\operatorname{EFF}(X)$ denote the effective cone.

Nagata's numerical inequality. If

$$dL-m(E_1+\cdots+E_r)\in\operatorname{EFF}(X),$$

then $d>m\sqrt r$.

The source states this as an equivalent formulation of Nagata's conjecture. It is known when $r$ is a square, but remains open for general $r>9$.