Say we imagined a mathematical model so detailed that it completely describes a universe like our own. Now if we simulated such a universe on a futuristic supercomputer then obviously the beings inside will exist in a sense. On the other hand if we don't ever simulate the model, and in fact there are an infinite number of possible abstract universes, then do the beings inside these abstract universes exist? Do you think we are possibly only abstract mathematical existence ourselves?
My answer would be yes, the universe could be simply a mathematical abstraction.
Why? Because I have never heard about a proof that refutes your question (title). In fact, I've read in magazines -- a very long time ago (when the movie Matrix was popular) -- that we cannot refute the hypothesis that we live inside a simulation.
In other words: "the universe could be simply a mathematical abstraction" is a valid hypothesis. Today, we are unable to disprove it.
Regarding your other question (body - "can we create our own simulation?"): my answer would be no.
It has to do with the fact that it is computationally and physically impossible to run a simulation -- complete, perfect, lossless, bit precise -- of our universe from inside our universe (please someone verify that sentence, as I'm not 100% sure about that, it's just vague memory).
I'll quote myself (curiously, I've written down the following a few days ago):
The simulated beings will never have enough computational power to run a complete and perfect simulation like the simulation inside which they live.
Again, I might be completely wrong. But if I'm not wrong, I'll be very happy because I like that quote (I've written it down for a reason :)
You don't even need to go so far as a futuristic supercomputer-powered universe simulation to get the idea that maybe we're all just bits of code living in an artificial realm.
Video games today include NPCs that interact with players (and eachother) based only on what that object can "sense", and interact with their virtual environment in novel ways to satisfy programmed "needs" (think SIMs going to the bathroom, or FPS NPCs running for health power ups when at low HP).
Now advance those kinds of behaviors a couple of generations. You could have NPCs with no direct access to information beyond that which their "senses" bring in, and not necessarily aware of their artificial status.