The finite-field sharp exceptional-set conjecture in three dimensions

Let $A\subset\mathbb{F}_p^3$ satisfy

$$\#A=p^a.$$

Recall the exceptional set $E_s(A)$ for projection to lines or planes. Let $t(a,s)$ be the lower bound for $T(a,s)$ given by Proposition 1 for projections to lines, or by Proposition 2 for projections to planes. Finite-field sharp exceptional-set conjecture. In either case,

$$\#E_s(A)\leq C_{\epsilon,a,s}p^{\epsilon+t(a,s)}.$$

This conjecture transfers the proposed sharp Euclidean exponents to projections in $\mathbb{F}_p^3$ and predicts that the explicit examples determine the exceptional-set size up to an $\epsilon$-loss. The source does not give evidence of resolution, so the conjecture remains open.