Existence of superregular matrices over fields of size $2^{\gamma-2}$

Let $b3\geq 5$. A $b3\times b3$ matrix over the finite field $\mathbb{F}_{2^{\gamma-2}}$ is superregular if every nontrivial minor is nonzero.

Superregular matrix existence conjecture. For every integer $b3\geq 5$, there exists a $b3\times b3$ superregular matrix over

$$\mathbb{F}_{2^{\gamma-2}}.$$

The conjecture would significantly improve the general upper bound on the field size required for constructing superregular matrices, which in turn are used to construct convolutional codes with a maximum distance profile. The paper presents it based on computer searches; its status is not resolved in the supplied text.