Big Cube Reduction

4⁴ with paired 1c centers

Just like 3D reduction of big cubes, higher dimensional reduction works by pairing up groups of pieces with more and more colors until the n^d is reduced into an (n-1)^d. Pairing up pieces is done in a very similar way to the 3D method; If you can solve 3³, 4³, and 3⁴, then you can solve 4⁴.