Dvoretzky-Rogers equality conjecture for the reverse isodiametric problem

Let $\operatorname{DR}(m,n,j)$ denote the Dvoretzky-Rogers-type volume quantity used in the paper. The relevant parameter choice is $m=\binom{n+1}{2}$, $j=n$, in dimension $n$.

Dvoretzky-Rogers equality conjecture. For every $n\in\mathbb{N}$,

$$\operatorname{DR}\left(\binom{n+1}{2},n,n\right)=\frac{\sqrt{n+1}}{n!\,2^{\frac n2}}.$$

This equality would imply the general-case part of Makai Jr.'s reverse isodiametric conjecture. The surrounding results provide lower bounds for the Dvoretzky-Rogers quantity and show that the conjectured value would yield the desired reverse isodiametric bound; whether equality holds remains open.