The uniform domination conjecture for Steiner triple systems

Let $STS(v)$ denote a Steiner triple system of order $v$, and let $\gamma(D)$ be the domination number of its incidence graph.

Uniform domination conjecture. There exists a function $f:\mathbb{N}\rightarrow\mathbb{N}$ such that, if $D\in STS(v)$, then

$$\gamma(D)=f(v).$$

Equivalently, the domination number depends only on the order $v$, not on the structure of the Steiner triple system. The conjecture is verified for $v\leq 15$, but remains open in general.