Tables of sizes of small complete arcs in the plane PG(2,q), q 190027, obtained by an algorithm with fixed order of points (FOP)
Daniele Bartoli, Alexander A. Davydov, Giorgio Faina, Stefano Marcugini, Fernanda Pambianco · arXiv (Cornell University) · 2014
In the recent works of the authors, an algorithm FOP using any fixed order of points in PG(2,q) is proposed for constructing small complete arcs. The algorithm is based on an intuitive postulate that PG(2,q) contains a sufficient number of relatively small complete arcs. Also, in these works, it is shown that the type of order on the points of PG(2,q) is not relevant. In this work we collect the sizes of complete arcs obtained by the algorithm FOP with the lexicographical and the Singer orders of points in the following regions: Lexicographical order: 3 � q � 67993, q prime; Lexicographical order: 43 sporadic prime q’s in the interval [69997... 190027]; Singer order: 5 � q � 40009, q prime.