This website refers to a class of groups as Omega groups. An example of such a group is $\Omega_4^+(\mathbb{F}_3)$. I have not found any other source that uses this terminology, nor am I able to discern how these groups could be defined. They appear to be further subclassed into Omega groups of $+$ type and of $-$ type, and there is a notion of a projective Omega group.
For $n\in\mathbb{N}$ and a field $F$, how does one define $\Omega_n^+(F)$ and $\Omega_n^-(F)$?
I would assume that these are subgroups of $\mathrm{GL}_n(F)$. If this is the case, what matrices comprise the Omega groups? What matrices generate the Omega groups?