Complete Arcs and Surfaces in Three Dimensional Projective Space PG(3,7)

Abstract

The purpose of this thesis is to construct surfaces and complete arcs in the projective 3-space over Galois fields GF(q), q = 7. A(k,n)-arc in is a set of k points; no n + 1 of them are coplanar. A(k,n)-arc is complete if it is not contained in a (k + 1, n)-arc. In this work the (k,¶)-span are constructed in and it is found that, it exists in when k = 50. Moreover, the maximum (k,¶)-span, is called a spread.