This hypothesis is really fun to play with when you know just enough computer and physical science to get yourself into trouble.
Beyond requiring a universal speed limit any model of the universe would also require that no measured value can be on an infinitely divisible scale. This is because if a measurable value in our universe could be any arbitrary value it would then require infinite data to store that value in the simulator.
Consider a wanting to measure something that is less than a meter, with a meter-stick of course. You can first take a measurement based on tenths of a meter and represent this approximate value with the one digit numbers 0-9. Measuring hundredth of a meter and you can approximate with the two digits numbers 00-99. But no matter how many times you divide your unit of measure by ten the true length of the object can still fall between the two closest measurable values. Thus with any finite number of digits you cannot guarantee a truly accurate measurement.
The obvious solution for the simulator is to define some absolute minimum distance. Then any length or position must fall perfectly on a multiple of this distance and can be perfectly represented by a finite value (unless you have an infinite length or distance).
And guess what... Some guy called Max Planck showed, indirectly, that their is such a minimum distance*, now know as the Planck length which is about 1.6 × 10^-35 meters. Or 1.6 divided by ten 35 times, small enough that you probably haven't noticed this limit it recently.
The fun with physics continues if you consider the implications of having a maximum speed and a minimum possible distance. At the speed of light it will still take about 5.4 × 10^-44 seconds (5.4 divided by ten 44 times) to cross the Planck length and this length of time is called the, you guessed it, Planck time. If you have two moments in time that are closer together than this length then by definition nothing can have moved in between those two moments. Thus perfectly accurate time values can by stored with a finite value, as long as time itself is finite.
Mass too must have a minimum unit as special relativity tells us that mass and energy are interchangeable (remember E = MC^2) and quantum mechanics gets its name from the fact that the quanta is a smallest unit of energy possible.
Conveniently with basic values for mass/energy, distance and time you can derive all other units of measure.** This means that any value that has an non-infinite range of possible values can be accurately stored as a finite number.
Science tells us that space may in fact be finite, but we don't know about time yet. Luckily it doesn't matter! The beings in charge of hte simulator don't need to store the exact state of the universe at all points in time. All they need to do is store 5 values for each and every particle in the universe: what type of particle it is, X,Y and Z coordinates and it's current velocity (velocity being it's speed AND direction). Then you just iterate from on moment of time to the next by your unit of Planck time forever, throwing out all the old data each step.
Physics, what a beautiful thing.
PS - All this is based off of A) my interpretation what smart people have written and B) really confusing stuff.
I think that the easiest way to make sense of this is to consider all objects as moving at constant speed through 4-D spacetime. Thus faster you travel in the physical dimensions, the slower you travel through time. If you quantize the "distance" you travel in spacetime and take into account relativistic time and length dilation then things work out, well... beautifully.
* I think it's more accurate to say that any two objects that are separated by less than this distance cannot be compared to each other in normal ways. It would be useless in ALL practical senses to view either object as being in front of, behind, above, below, windward, or leeward of the other object.
** I think, I'm not really sure why. Probably that pesky common sense thing.