Finite projective planes

Related pages

Subplanes of finite projective planes
The small projective planes
If is a finite projective plane, then the order n of obviously is finite, too, and we have the following counting formulas.

In particular, is a S(n2+n+1,n+1,1) Steiner system, i.e. a 2-(n2+n+1,n+1,1)-design.

If q is a prime power, then the projective plane over GF(q) is a finite projective plane of order q. In fact, all known finite projective planes are of prime power order. Unfortunately, there is only one known theorem excluding a great range of values for the order n, namely the Bruck-Ryser theorem. The following things are commonly conjectured.

Note that there exists a finite projective plane of order n if and only if there exists a finite affine plane of order n. The exact number of isomorphism types of projective planes of order n is only known for a few small values of n.

See also

Contributed by Hauke Klein
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