The Gamma-bound dominance conjecture for integer D-optimality

Let $s$ and $q$ be the parameters defining the feasible bounds in the integer D-optimality formulation, and let \mathfrak{z}_{\text{tiny \Gamma}} and \mathfrak{z}_{\text{tiny \mathcal{H}}} denote the corresponding objective bounds.

Gamma-bound dominance conjecture. For $s-q\geq 1$, we have

$$\mathfrak{z}_{\text{\tiny $\Gamma$}}\leq \mathfrak{z}_{\text{\tiny $\mathcal{H}$}}.$$

The conjecture is motivated by numerical experiments: equality is observed when $s=1$, while strict inequality is always observed when $s>1$. The paper presents this as a conjecture based on those experiments; no proof or resolution is supplied.