Goddard–Henning conjecture on independent domination in cubic graphs

Let $G$ be a connected cubic graph of order $n$, and let $i(G)$ denote its independent domination number. Reed's bound concerns domination in cubic graphs, and the exceptional graphs here are $K_{3,3}$ and the $5$-prism $C_5 \mathbin{\Box} K_2$.

Goddard–Henning conjecture. If

$$G \notin \{K_{3,3}, C_5 \mathbin{\Box} K_2\},$$

then

$$i(G) \leq \frac{3}{8}n.$$

The conjecture asks whether Reed's $\frac{3}{8}$ upper bound for the domination number extends to independent domination, apart from the two stated exceptions. The supplied source presents it as a conjecture; its resolution is not specified here.