The what, how and why of finite projective planes

Abstract: This thesis defines the finite projective plane and the affine projective plane. A method of construction is defined for the field planes by extension of the affine plane constructed from the vector space over a finite field. The thesis explores for which orders planes can and cannot be constructed, in particular, for the prime powers there exist planes. For n=6 a computer search is conducted using a recursive algorithm, which shows that n=6 is not possible as an order for finite projective plane. The thesis then illustrates an application for finite projective planes in the form of a threshold scheme for secret sharing.