Kantor's conjecture on the abundance of additive MRD codes

Let $p$ be prime and let $n$ be a positive integer. Consider additive MRD codes in $M_{n\times n}(\mathbb{F}_p)$ with minimum distance $n$, where equivalence is taken under the usual rank-metric code equivalence. Kantor's conjecture. (1) The number of equivalence classes of such additive MRD codes is not bounded above by a polynomial in $p^n$. (2) There is an exponential number of equivalence classes of such additive MRD codes. This concerns the ubiquity of MRD codes: despite the known classifications in small parameters, the number of inequivalent additive MRD codes is expected to grow very rapidly. The source presents this as an open conjecture, paraphrased from Kantor (2006).