Superlinear blocker-number conjecture

Let $b(n)$ be the minimum integer such that some set of $n$ points in the plane in general position is blocked by a set of $b(n)$ points. Superlinear blocker-number conjecture.

$$\frac{b(n)}{n}\rightarrow\infty\quad\text{as }n\rightarrow\infty.$$

Known lower bounds are linear, including $b(n)\geq 2n-3$ and $b(n)\geq(\frac{25}{8}-o(1))n$; the conjecture that $b(n)$ is super-linear remains open.