Bickle–White conjecture on attaining the genus-sum lower bound

Let $G$ be a graph of order $n$, let $\overline{G}$ be its complement, and let $\gamma(G)$ denote the genus of $G$. For $n\geq 11$, consider the lower bound

$$\left\lceil \frac{1}{12}\left(n^{2}-13n+24\right)\right\rceil$$

for $\gamma(G)+\gamma(\overline{G})$. Bickle–White conjecture. For every $n\geq 11$, there is a graph $G$ for which

$$\gamma(G)+\gamma(\overline{G})=\left\lceil \frac{1}{12}\left(n^{2}-13n+24\right)\right\rceil.$$

Bickle and White established the lower bound and showed that it is attained for orders $n=12s+11$ and $n\in\{13,25,37,49\}$; Sun later showed attainment for $n=24s+13$. The conjecture asks for attainment at every order $n\geq 11$.