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Using a SAT-solver on top of a partial previously-known solution we improvethe upper bound of the packing chromatic number of the infinite square latticefrom 17 to 15. We discuss the merits of SAT-solving for this kind of problem aswell as compare the performance of different encodings. Further, we improve thelower bound from 12 to 13 again using a SAT-solver, demonstrating theversatility of this technology for our approach.

The packing chromatic number of the infinite square lattice is between 13 and 15