The problem is motivated by generalizing Moore graphs, graphs with maximum possible girth ($2\text{diam}+1$) given the diameter.

**Question.** Does there exist a graph $G$ with $\text{g}(G)-\text{diam}(G)>8$ and minimum degree at least $3$, where $\text{g}(G)$ and $\text{diam}(G)$ are the girth and diameter of $G$, respectively?

**Remark.** There's an infinite class of graphs with $\text{g}(G)-\text{diam}(G)=8$: the (point,line) incidence graphs of generalized octagons have $\text{g}(G)=16$ and $\text{diam}(G)=8$.

Bonus points (+200 bounty) for a proof that $\text{g}-\text{diam}$ is unbounded for graphs with minimum degree at least $3$.