Alexander A. Davydov, Giorgio Faina, Stefano Marcugini, Fernanda Pambianco
Published 2010-04-16, updated 2010-08-28Version 5
New upper bounds on the smallest size t_{2}(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 t_{2}(2,q)<4.5\sqrt{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.
On sizes of complete arcs in PG(2,q)
Upper bounds on the smallest size of a complete arc in the plane PG(2,q)
Tables, bounds and graphics of the smallest known sizes of complete arcs in the plane $\mathrm{PG}(2,q)$ for all $q\le160001$ and sporadic $q$ in the interval $[160801\ldots 430007]$
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