## z(4,4 | 4,4) = 64

$I$ | $I$ | $I$ | $\alpha$ |

$I$ | $\beta$ | $\alpha\beta$ | $I$ |

$\alpha\beta$ | $I$ | $\beta$ | $I$ |

$\beta$ | $\alpha\beta$ | $I$ | $I$ |

$I$ is the identity, and $\alpha,\beta$ generate $\mathbb{Z}_2 \times \mathbb{Z}_2$. The $I$ entries form an extremal rectangle-free matrix, showing that the finite projective plane of order 4 is sub-similar.

$I$ | $I$ | $I$ | $I$ |

$I$ | $\alpha$ | $\beta$ | $\alpha\beta$ |

$I$ | $\beta$ | $\alpha\beta$ | $\alpha$ |

$I$ | $\alpha\beta$ | $\alpha$ | $\beta$ |

The quotient matrix for the finite projective plane of order 4. $I$ is the identity, and $\alpha,\beta$ generate $\mathbb{Z}_2 \times \mathbb{Z}_2$.

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