Finite projective planes and the Delsarte LP-bound

2018/01/29 by Matolcsi, Mate, Weiner, Mihaly
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1801.09480

Abstract

We apply an improvement of the Delsarte LP-bound to give a new proof of the non-existence of finite projective planes of order 6, and uniqueness of finite projective planes of order 7. The proof is computer aided, and it is also feasible to apply to higher orders like 8, 9 and, with further improvements, possibly 10 and 12.

Related

• Character tables and the problem of existence of finite projective\n planes
• Existence of Projective Planes
• Finite Projective Planes
• Combinatorial problems in finite geometry and lacunary polynomials
• New necessary conditions for the existence of finite non-Desarguesian flag-transitive projective plane