What AdS/CFT implies is the opposite: That all the information needed to describe a 3D space can fit in a 2D space, like a hologram. This is astounding and extremely counterintuitive.
The hitch is that our universe is (probably) not AdS; it's dS. And the astounding math doesn't work for the de Sitter space we live in.
I'm not totally certain about this but I think you skipped over something important.
It's not that 3D space can be described by 2D space, it's that _our_ "3D" space appears to fit in 2D space because every time the universe puts too much information in the 3D space we get a black hole and a black hole is a 2D surface in 3D space.
The tiny black holes that are suggested by non renormalizability are one of the mysteries that make AdS/CFT an attractive direction in which to explore our own universe, partially because Susskind has already shown that black holes in our universe can be described by their surfaces.
The actual dimensionality is 4D to 3D once you add in time. But the math basically says an nD hyperbolic conformal manifold (AdS) can be completely described by its nD-1 boundary (CFT).* So I think it works in any number of dimensions.
*Oversimplified and probably wrong, but probably close enough for this discussion.