On k-caps in PG(n, q), with q even and n ≥ 4

2017/10/06 by Thas, Joseph A.
#05B25 #51E20 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1710.02512

Abstract

Let m₂(n, q), n ≥ 3, be the maximum size of k for which there exists a complete k-cap in PG(n, q). In this paper the known bounds for m₂(n, q), n ≥ 4, q even and q ≥ 2048, will be considerably improved.

Related

• On k-caps in PG(n, q), with q even and n ≥ 3
• Tables, bounds and graphics of the smallest known sizes of complete caps in the spaces PG(3,q) and PG(4,q)
• Bounds on sizes of general caps in AG(n,q) via the Croot-Lev-Pach polynomial method
• New inductive constructions of complete caps in PG(N,q), q even
• Upper bounds on the smallest size of a complete cap in PG(N,q), N≥3, under a certain probabilistic conjecture