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Let $\mathcal{A}$ be an axiomatic affine plane. First let $\mathcal{A}$ be finite. Suppose that the automorphism group of $\mathcal{A}$ acts transitively on nonincident point-line pairs (that is, on ...

As I understand, there is a $3$-dimensional analogue of Segre's theorem stating that the maximum size of a set in ${\bf F}_q^3$ ($q$ odd) with no three points collinear is $q^2+1$. I am trying to ...