If we think of spacetime as some sort of cellular automaton, where each state of a given point is a function (with some randomness, because God likes to throw dice) of previous states of the surrounding points, if the rules for a new state generation are extremely complex, there will be some significant overhead in dimensions we don't see, because the rules need to be somehow represented outside the observable reality. Another issue with this idea is that while the rules might be "outside", the parameters themselves have to be somehow encoded in the state of a cell, and can't propagate faster than light, or one cell (an indivisible unit of space) per indivisible unit of time), which limits the number of parameters accessible to any given cell to the ones immediately surrounding it.

Disclaimer: I hope it's obvious, but I'm no physicist. This is just how I would build a universe.