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In page Projective plane:
"The existence of finite projective planes of other orders is an open question. The only general restriction known on the order is the Bruck–Ryser–Chowla theorem that if the order N is congruent to 1 or 2 mod 4, it must be the sum of two squares. This rules out N = 6. The next case N = 10 has been ruled out by massive computer calculations.[1] Nothing more is known; in particular, the question of whether there exists a finite projective plane of order N = 12 is still open.[citation needed]
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