The quartic growth conjecture for radial orderings

Let $g(n)$ denote the minimum number of distinct radial orderings determined by a set of $n$ points in strong general position in the plane. Quartic growth conjecture.

$$g(n)=\Theta(n^4).$$

The paper proves bounds of $\Omega(n^3)$ and $O(n^4)$, so this conjecture asks to close the remaining gap.