Araujo-Pardo–Leemans family conjecture for edge-girth-regular graphs

Let $egr(v,k,g,\lambda)$ denote an edge-girth-regular graph with $v$ vertices, valency $k$, girth $g$, and each edge contained in exactly $\lambda$ cycles of length $g$. Let $q\geq 3$ be a prime power and let $g\in\{8,12\}$. Araujo-Pardo–Leemans conjecture. There exists a family of

$$egr\left(2q^{\frac{g-2}{2}},q,g,(q-1)^{\frac{g-2}{2}}(q-2)\right)$$

graphs, and these graphs are extremal edge-girth-regular graphs, meaning that they attain the minimum possible order for their parameters. The conjecture proposes infinite families in the cases $g=8$ and $g=12$. The paper states that its computations disprove the conjecture for cubic graphs of girths $8$ and $12$, so the conjecture is refuted as stated.