Might be - I think one of the recent theories (that comes out of certain approach to quantum gravity) is that our universe might come out as consequence of (badly) written error correction code for some quantum computer.

Yes, but that simulation is based on the existence of Mathematics, not something that someone has written on a computer.

As the Ancient Greeks postulated, Mathematics itself just exists, because it is a theoretical concept, not something that needs to be invented.  Mathematics cannot "not exist".

That's why I said 'some kind' of simulation. We can only think within the limitations of this universe and its laws, we have no idea what kind of 'tech' the authors of this simulation have and use.

There is no evidence because we are living in a bubble. Imagine if a video game character stepped out of the game into our world where laws are completely different.

I don't think that the usual ideas of simulating things work well with the Mathematical Universe Theory.  You can calculate that 1 + 1 is 2, but what does it mean to simulate the fact that 1 + 1 is 2?

You are correct that it's entirely possible that there is another layer, possibly even infinite supersets of what we know of as Mathematics that we have no possibility of examining because it just doesn't work here.  

For what it's worth, Plato discussed whether Mathematics was real and/or different to the real world, and if it was invariant in time.  Max Tegmark did work trying to show that the Universe does exactly what static Mathematics tells it to.  Lots of people have theorised why Mathematics exists and works at all.  I personally like the approach of "mathematics can't not exist, and that's why we're here".

Another thing I forgot to mention in my post the other day is, if our universe really is some sort of advanced construct, then what of the universe the people who made the simulation? Is their universe natural, or is it too artificial? Is it simulations all the way down? Like I said before, it really does seem like a secular creation myth. It's like some people can't deal with the likelihood that existence is quite possibly a cosmic accident, that there may be no "why" to existence and that it simply *is* for reasons we may never know. The universe was never under any obligation to conform to our psychological needs or our notions of "common sense." But some people need to feel like they and everything else exists on purpose.

Impossibur. For example the Moon was put exactly where it is, if it was anywhere else the Earth would be basically inhabitable, at least by humans. Can it be a chance? No way. It was either put there by the creators of this simulation or by an advanced civilization before us.

Not with that attitude.

Once simulations are detailed enough to simulate a colony of ants in the space needed, asides from the particles needed the environment doesn't even need to be detailed, just enough to fool the ants I would think that would be enough to sway me in the direction of yes.