New largest bounds of (

Abstract

A projective plane is defined as a structural geometry comprising points and lines related through a specific mathematical relationship. As a case study, a projective plane of order (ω) is considered in this research, including a number of points signified by a quadratic equation (ω2+ ω +1) and a number of lines signified by the same equation and represented by PG(2,ω). Each line can convey (ω +1) points, and each point can pass through (ω +1) lines. The blocking set S is defined by a group of points, where every single line can have at least ℓ points of S, and other lines can have exactly ℓ number of points of S. It is worth noting that the blocking set S is a complementary part of a (d,m)-arc D taking into account that ℓ=ω+1−m. In short, this study aims to prove that (d,m)-arcs are not existing at ω equal to seventy nine.