I spent some time thinking about this in college, the problem you run into is the sheer size of the lookup table, you will get higher complexity in the ability to search this table (or prep your input matrix to be searchable).

I'm going to try and remember the calculations I performed, but I remember just looking at permutations/combinations of 8bit integer matrices, 2x2 seems reasonable but 3x3 or 4x4 gets unreasonable from an algorithmic/memory perspective very quickly