The W1–G2 maximal cross-correlation conjecture in non-Germain prime fields

Let $p\neq 19$ be a prime other than a Germain prime. Let $f_1$ and $f_2$ be $W_1$ permutations, and let $f'_1$ and $f'_2$ be $G_2$ permutations, all generated in the finite field $\mathbb{F}(p)$. Write $\Psi_{f_1,f_2}(u,v)$ and $\Psi_{f'_1,f'_2}(u,v)$ for the corresponding cross-correlations at shifts $(u,v)$.

W1–G2 cross-correlation conjecture.

$$\max_{(u,v)}\max_{(f_1\neq f_2)}\Psi_{f_1,f_2}(u,v)=\max_{(u,v)}\max_{(f'_1\neq f'_2)}\Psi_{f'_1,f'_2}(u,v)+1.$$

This is the combined strong conclusion of the preceding conjectures and theorems: the maximal cross-correlation for $W_1$ arrays exceeds that for $G_2$ arrays by one. The source presents it as conjectural and gives no resolution.