Finite projective planes
is a finite projective plane, then
the order n of
obviously is finite, too, and we have the following counting formulas.
is a S(n2+n+1,n+1,1) Steiner system,
i.e. a 2-(n2+n+1,n+1,1)-design.
for each line
for each point
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
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.
Contributed by Hauke Klein
Version $Id: finprojective.html,v 1.2 2001/01/02 19:41:04 hauke Exp $