Let $X$ be a finite set of points in $\mathbb{P}^3$ of cardinality $\ge 3d +3$ which fails to impose independent conditions on sections of $\mathcal{O}(d)$ and $X$ does not pass through any quadratic hypersurface. Can we give an effective bound on cardinality of a subset $Z \subset X$ such that there exist a hyper plane containing $Z$ ?
If $|X| < 3d + 2$, then it is known that either there exist a line containing at least $d+2$ points of $X$ or there is a plane containing at least $2d+2$ points of $X$.
