The small projective planes

For the small values of n, the exact number of isomorphism types of finite projective planes of order n is known.

v Isomorphism types
2 1
3 1
4 1
5 1
6 0
7 1
8 1
9 4
10 0

That there exists no projective plane of order 6 is a consequence of the Bruck-Ryser theorem. The values up to n=7 may be verified by hand. The uniqueness of the projective plane of order 8 was proved by using a computer.

The four projective planes of order 9 were known for quite some time, but the proof that there doesn't exist another plane of this order, requires a computer.

Finally, the non-existence of the order n=10 needs pretty massive computer usage.

Contributed by Hauke Klein
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