The exhaustive search for the existence of a finite projective plane of a given order n can be very time-consuming even for small values of n. The troubled story of the case n = 10 (see [8]) does not seem to have discouraged attempts for the next values of
n for which non-existence is not covered by the Bruck-Ryser Theorem. Apart from the legitimate curiosity related to the prime
power conjecture, there might be other indirect reasons for wanting to investigate a specific value of n. Classification theorems
in finite geometries often have the shape of a general statement handling all but finitely many values of the involved parameter.
Typically, when dealing with planes, this parameter is the order of the plane.