Some Properties from Construction of Finite Projective Planes of Order 2 and 3

Abstract

In combinatorial mathematics, a Steiner system is a type of block design. Specifically, a Steiner system S(t, k, v) is a set of v points and k blocks which satisfy that every t-subset of v-set of points appear in the unique block. It is well-known that a finite projective plane is one examples of Steiner system with t = 2, which consists of a set of points and lines together with an incidence relation between them and order 2 is the smallest order. In this paper, we observe some properties from construction of finite projective planes of order 2 and 3. Also, we analyse the intersection between two projective planes by using some characteristics of the construction and orbit of projective planes over some representative cosets from automorphism group in the appropriate symmetric group.