Nagata's conjecture for homogeneous divisors

Let $X=X_{n,s}$ be the blow-up of projective $n$-space at $s$ general points, and let $D=dH-mE_1-\cdots-mE_s$ be a homogeneous divisor, with degree $d$ and common multiplicity $m$. Nagata's conjecture. If

$$\frac{d}{m}<\sqrt{s},$$

then $D$ is not effective. The supplied text gives no resolution status for this conjecture.