The Outside

 The Outside  is an space of nothingness that is outside the Omniverse, and it's diameter is equivalent to 100,000 ''Omniverses. Because of The Outside's configuration, it only consists of isolated pure existence-0 objects, which helps stop The Barrel from causing immense amounts of entropy and chaos due to the fact that things would stuff The Barrel'' and create a mess of sub-structures.

The Outside is here, because nothingness is an opposite parallel to existence, which implies that instead of nothingness forming chaos over time, nothingness forms order over time. These effects magnify as you get closer to edges of existence and nothingness due to stronger "competition". This explains why The Outside is so strict that it resists almost everything and even every nothing.

Escaping
Despite the strictness of this bubble of nothingness, there is a way to escape. If you manage to turn particles in a great enough radius around the edges of everything and every nothing into clumps of "nothing", then your distance to the edge will be compressed into 0, a point of infinite order and disorder. The order and disorder combines into a "meta-disorder", turning into a structure that is infinitely "ordered" and infinitely "disordered", which covers a wide enough scope that it breaks logic, allowing tunnels of customized laws and disorder that allow travel to The Barrel's outside, or if you are precise enough with the way you break logic barriers, even reaching the outside of The Box is possible. From this point, bigger structures can be traveled.

Malpractices
However, nowadays, reaching the outside of said box is getting harder and harder, and said difficulty accelerates. This is due to the fact that travels to The Outside have left glitchy regions that are corrupting both The Omniverse and The Outside, which deletes the more unstable regions of both by natural selection, leaving the more stable regions that are harder to break through.

Also, some groups have intentionally gone out to stabilize or destabilize the edges between both for various reasons, such as preventing entities from reaching high-level structures, or to trap entities in the edges between both verses. In addition, a common practice, called Entity Fishing, where entities are lured to the edges, only be erased in an infinitely strict world that destroys itself has been done. A material known as Logicium can be obtained through Entity Fishing. This material can override the laws of verses and structures.

Some entities have done this infamous practice so many times that they are able to bypass enough barriers to reach Nigh Ascendent Omni-God status, but nowadays, said title is hard to get due to traps and measures set up by Ascendent Omni-Gods, like Alphasm. In fact, only a group named Alpha managed to pull off the "upgrade" before the measures were put in place, being the discoverers of Entity Fishing themselves. Soon after they were upgraded, Alphasm, named after Alpha, which he ironically was trying to stop, would set up measures so difficult that only entities controlling more than the Nigh Omnipotence Barrier would be able to upgrade themselves to such an outrageous status.

Structures in the Outside

 * Imaginary Dodecahedra - Since Archverses are located all over the Omniverse, and Imaginary Dodecahedra bind Universes to make large-scale structures within Multiverses, it isn't all that uncommon for those located at the "edge" of the Omniverse to simply diffuse out the Omniverse. Since the Outside only contains existence-0 objects, the Universes it binds will be decoupled and left to wander in their Multiverse.
 * Universe matter - Sometimes, Universes deal with matter that breaks its laws of physics by changning its existence rank. Specifically, existence rank 0 is the most common one. In the same way that Imaginary Dodecahedra were mentioned, this matter can slowly diffuse out.
 * Particle globules - Rogue free-roaming particles will encounter many other particles and particle-like matter. If these particles and matter have attractive properties, they may created globules of random discarded particles along their journey. If such a globule gets large enough, it may start picking up non-particle debris. If these particles become non-existent along the way, or start off as being non-existent, they may make their way out of the Omniverse.
 * Primordial Imaginary Cubes - Primordial Imaginary Cubes were the equivalent of Imaginary Dodecahedra in the very early Omniverse. However, as the laws of the Omniverse slowly changed over time, Primordial Imaginary Cubes started slowly getting forcefully diffused through the Omniverse's barrier and wandering out, whilst regular Imaginary Cubes werent affected. Since their velocities were non-zero, and since so much time has passed, most Imaginary Cubes now reside in a cloud midway into the Outside.
 * Civilizational bases and modes of transport - There are many post-Omniversal civilizations residing within the Outside, as well as Omniversal ones that have research centers out there, and many simply wish to reside within voids and yet remain in close contact with the Omniverse, for whatever various reasons.