Sufficient conditions for discrete restriction estimates over $\mathbb Z/N\mathbb Z$

Let $n\geq 2$, let $1\leq r,s\leq\infty$, and write $r'$ for the Hölder conjugate of $r$. Let the discrete restriction estimate refer to the estimate defined earlier in the source. Sufficient-conditions conjecture for discrete restriction. If

$$r'\geq\frac{n(n+1)}{2}+1\qquad\text{and}\qquad r'\geq s\frac{n(n+1)}{2},$$

then the discrete restriction estimate holds whenever every prime factor $p$ of $N$ satisfies $p>n$. The preceding necessary conditions motivate this conjecture, while the source does not provide a proof or resolution.