Folklore conjecture on the order of regular graphs with prescribed girth

Let $g$ and $d$ be positive integers. A graph is $d$-regular if every vertex has degree $d$, its girth is the length of its shortest cycle, and its order is its number of vertices. Folklore conjecture. For every positive integers $g$ and $d$, there exists a $d$-regular graph $G$ of girth at least $g$ and order

$$\Theta\left((d-1)^{(\frac{1}{2}+o(1))g}\right).$$

The source describes this as a folklore conjecture related to the Moore bound and as the analogue of the preceding cubic-graph assertion for every fixed degree. The supplied status is unknown, so it remains open in this record.