Tables, bounds and graphics of the smallest known sizes of complete arcs in the plane PG(2,q) for all q≤160001 and sporadic q in the interval [160801… 430007]

2013/12/08 by Bartoli, Daniele, Davydov, Alexander A., Faina, Giorgio +3
#51E21 #51E22 (Primary) #94B05 (Secondary) #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1312.2155

Abstract

In the projective planes PG(2,q), we collect the smallest known sizes of complete arcs for the regions amp;all q≤160001,~~ q prime power;
amp;Q₄=\34 sporadic q's in the interval [160801…430007], see Table 3\. For q≤160001, the collection of arc sizes is complete in the sense that arcs for all prime powers are considered. This proves new upper bounds on the smallest size t₂(2,q) of a complete arc in PG(2,q), in particular \beginalign* t₂(2,q)&<0.998√(3qln q)<1.729√(qln q)& for &&7&≤ q≤160001;~~(1) t₂(2,q)&

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