The table becomes unwieldy on much simpler tasks than that.
Consider a 3x3 board where each cell holds 3 bits of information (each cell can be in 2^3 states). Then for the board you have (2^3)^9 = 2^27 different states.
Consider a 3x3 board where each cell holds 3 bits of information (each cell can be in 2^3 states). Then for the board you have (2^3)^9 = 2^27 different states.
Edit, I just considered : Unless you mean that the state is the combination of all the cells. Then you are right