for each line
for each point
Related pagesSubplanes of finite projective planesThe small projective planes |
is a finite projective plane, then
the order n of
obviously is finite, too, and we have the following counting formulas.
for each line
for each point
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.
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