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.

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