Kurz–Lätsch conjecture on oriented diameter and domination number

Let $G$ be a bridgeless graph, and let $\gamma(G)=\gamma$ be its domination number, where a dominating set is a vertex set $D$ such that every vertex in $V(G)\setminus D$ is adjacent to at least one vertex of $D$. Write $\overrightarrow{\operatorname{diam}}(G)$ for the oriented diameter of $G$.

Kurz–Lätsch conjecture. For every bridgeless graph $G$ with $\gamma(G)=\gamma$,

$$\overrightarrow{\operatorname{diam}}(G)\leq \left\lceil\frac{7\gamma+1}{2}\right\rceil.$$

Kurz and Lätsch had previously proved the upper bound $\overrightarrow{\operatorname{diam}}(G)\leq 4\gamma$. Their conjecture seeks a sharper universal bound in terms of the domination number; the supplied source gives no resolution.