You're indisputably right about needing exactly as many bits in the simulation as are in the real universe, if you define "simulation" as a complete 1:1 reproduction. That raises certain philosophical questions about the status of the simulation--is it "really unreal", is it a "copy", is it another universe that will evolve forward from the point of branching?

But there are less-absolutist definitions of a simulation. Simulation and game designers have been forced by hardware constraints to develop a wide range of computational shortcuts. There's algorithmic texturing, tiling (create a pattern or object once, then copy it), fractals to create variations on a theme using just stored coefficients, etc.

And then there's the "if a tree falls in the forest..." dodge: Create the simulation only where there's an observer and only where the observer is looking.

Hmmm...could the "observer effect" be evidence that we are in fact living in a simulation? Are the existence of Planck limits and "quantum-ness" in general simulation artifacts?

Maybe a "real" universe would be analog rather than digital? In other words, if an analog universe could be said to require an infinite number of bits to completely describe, a simulation of it would be digitized and quantized to produce an approximation in a finite (if very large) number of bits.

Could our physics be a description of the simulation rather than a real universe?