Explicit basis conjecture for general linear invariants in all ranks

Let ${\mathcal{Q}}_m(n)=\mathbb{F}_q[x_1,\ldots,x_n]/(x_1^{q^m},\ldots,x_n^{q^m})$, let $G_n=GL_n(\mathbb{F}_q)$, and let $\delta_{s+1;m}$ and $\Delta_s^m$ be the operators and Dickson-algebra subspaces defined in the source. For $0\leq s\leq\min(m,n)$, consider the family

$$\delta_{s+1;m}^{n-s}(f),\qquad f\in\Delta_s^m.$$

Explicit general-linear basis conjecture. The set $\mathcal{B}_m(n)$ consisting of these elements forms an $\mathbb{F}_q$-basis of ${\mathcal{Q}}_m(n)^{G_n}$. The conjecture is the full-general-linear specialization of the proposed parabolic basis and would give an explicit description of all invariants. The source gives no resolution status.