Let $\mathrm{gnu}(n)$ denote the number of groups of order $n$.
I'm aware that we know $\mathrm{gnu}(2^{10})$, but not $\mathrm{gnu}(2^{11})$. Also, we know functions describing $\mathrm{gnu}(p^{1}), \dots, \mathrm{gnu}(p^{7})$ for $p$ prime in terms of PORC functions.
This paper states $\mathrm{gnu}(3^{9})$ is known. I can't find anything on $\mathrm{gnu}(3^{10})$. Presumably, this is unknown as of December 2023, is that correct?
I can't find any sources for $\mathrm{gnu}(5^{8})$ or higher prime bases to the power of $8$. Are these, as of December 2023, also unknown?