@blackle You want to partition the 2^(8^2) states into 8^2 classes such that every class has an element a distance at most 1 from any given 2^(8^2).

I think we can do this by trying to communicate which row and which column it's under separately? e.g. with some sort of function on, maybe, the number of heads in each row? And we take that mod 8 to get the row of the star, and do that on cols for col of it.