Langer's asymptotic conjecture for cusps on plane curves

Let $k_{\max}(d)$ be the maximal number of ordinary cusps of a plane curve of degree $d$. Langer's conjecture.

$$\lim_{d\to\infty}\sup\frac{k_{\max}(d)}{d^2}=\frac{125+\sqrt{73}}{432}.$$

This conjecture asserts that the coefficient of $d^2$ in the known upper bound for the number of cusps is sharp. The source presents it as an open asymptotic existence problem for cuspidal plane curves.