GPT-6 Astra raises MOLS lower bounds at 33 orders, and order 22 finally reaches four squares
Lower bounds on mutually orthogonal Latin squares (MOLS) have long lagged far behind upper bounds at orders that are not prime powers. Using established techniques including difference matrices, quasi-difference matrices, orthogonal-array lifting and projective-plane point selection, OpenAI's GPT-6 Astra constructed larger MOLS sets at 33 orders between 22 and 494, raising their lower bounds; at order 22 it produced 4 MOLS for the first time, so combined with existing results every order from n=22 upward is known to admit at least 4.