Exponential flow-count conjecture for 3-edge-connected graphs

Let $G=(V,E)$ be a 3-edge-connected oriented graph of order $n$, let $\text{?}$ be an abelian group with $|\text{?}| \text{?} 6$, and let $f:E\to\text{?}$. A flow $\text{?}:E\to\text{?}$ avoids $f$ if $\text{?}(e)\ne f(e)$ for every $e\in E$.

Exponential flow-count conjecture. There exists a fixed constant $c>1$ such that, for every such $G$, $\text{?}$, and $f$, there are at least $c^n$ flows $\text{?}$ avoiding $f$.

The paper presents this as a conjectural strengthening of its counting theorem, which gives exponential many avoiding flows for group orders at least $8$ but only existence for orders $6$ and $7$. Its status is not resolved in the supplied material.