Asymptotic enumeration conjecture for extremal and threshold matrices

Fix $n$. Let $M(d,n)$ be the number of nonequivalent $d$-dimensional extremal matrices of order $n$, and let $T(d,n)$ be the number of nonequivalent $d$-dimensional threshold matrices of order $n$.

Asymptotic enumeration conjecture. There is a constant $c=c(n)$ such that, as $d\to\infty$,

$$\log M(d,n)=c d^2(1+o(1))$$

and

$$\log T(d,n)=c d^2(1+o(1)).$$

The conjecture proposes matching quadratic-logarithmic asymptotics for the numbers of extremal and threshold matrices of each fixed order. The source presents these estimates as expected lower bounds, while the supplied material gives no resolution status.