Improved Bounds on mr(2, q) q=19, 25, 27. (13th March 2013)

• Record Type: Journal Article
• Authors: Daskalov, Rumen; Metodieva, Elena
• Other Names: Moukrim Aziz Academic Editor.
• Is Part Of: Journal of discrete mathematics. Volume 2013(2013)
• Publication Date: 2013-03-13
• Subjects: Computer science -- Mathematics -- Periodicals; Computer science -- Mathematics; Periodicals; 511.1
• DOI: 10.1155/2013/628952
• Languages: English
• ISSNs: 2090-9837

Abstract

Abstract : An (n, r )-arc is a set of n points of a projective plane such that some r, but no r + 1 of them, are collinear. The maximum size of an (n, r )-arc in PG(2, q ) is denoted by m r (2, q ). In this paper, a new (286, 16)-arc in PG(2, 19), a new (341, 15)-arc, and a (388, 17)-arc in PG(2, 25) are constructed, as well as a (394, 16)-arc, a (501, 20)-arc, and a (532, 21)-arc in PG(2, 27). Tables with lower and upper bounds on m r (2, 25) and m r (2, 27) are presented as well. The results are obtained by nonexhaustive local computer search.