New sizes of complete arcs in PG(2,q)

2010/04/16 by Alexander A. Davydov, Davydov, Alexander A., Giorgio Faina +5
Computer Science · Mathematics · Medicine · #Chronic Myeloid Leukemia Treatments #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #math.CO

paper · pdf · doi:10.48550/arxiv.1004.2817

10 pages

openalex publication_date 2010/04/16 · arxiv created 2010/08/28 · arxiv updated 2010/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

New upper bounds on the smallest size t₂(2,q) of a complete arc in the projective plane PG(2,q) are obtained for 853<= q<= 2879 and q=3511,4096, 4523,5003,5347,5641,5843,6011. For q<= 2377 and q=2401,2417,2437, the relation t₂(2,q)<4.5√(q) holds. The bounds are obtained by finding of new small complete arcs with the help of computer search using randomized greedy algorithms. Also new sizes of complete arcs are presented.

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