New largest bounds of (????, ????)-arcs in projective plane of order seventy- nine Authors Names

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.