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Journal of Discrete Mathematics
Volume 2013 (2013), Article ID 628952, 7 pages
http://dx.doi.org/10.1155/2013/628952
Research Article

Improved Bounds on

Department of Mathematics, Technical University of Gabrovo, 5300 Gabrovo, Bulgaria

Received 8 November 2012; Accepted 3 February 2013

Academic Editor: Aziz Moukrim

Copyright © 2013 Rumen Daskalov and Elena Metodieva. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

An ()-arc is a set of n points of a projective plane such that some r, but no of them, are collinear. The maximum size of an ()-arc in PG(2, q) is denoted by (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 (2, 25) and (2, 27) are presented as well. The results are obtained by nonexhaustive local computer search.