Finite affine planes

Related pages

The small affine planes
Let be a finite affine plane. If n is the order of , then the following counting formulas hold. In particular, is a S(n2,n,1) Steiner system, i.e. a 2-(n2,n,1)-design.

There exists a finite affine plane of order n if and only if there is a projective plane of order n. If all projective planes of order n are known, the affine planes of order n are exactly the affine derivatives of these planes. In particular, the isomorphism types of affine planes of order n correspond to orbits of lines under the automorphism groups of projective planes of order n.

In practice, the exact number of ismorphism types of affine planes of order n is only known for a few small values of n.

See also

Contributed by Hauke Klein
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