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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 mr(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 mr(2, 25) and mr(2, 27) are presented as well. The results are obtained by nonexhaustive local computer search

journal of discrete mathematics

Improved Bounds on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:msub><mml:mi>m</mml:mi><mml:mi>r</mml:mi></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mi>q</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:mi>q</mml:mi><mml:mo>=</mml:mo><mml:mn>19</mml:mn><mml:mo>,</mml:mo><mml:mn>25</mml:mn><mml:mo>,</mml:mo><mml:mn>27</mml:…

Improved Bounds on mr(2,q) q=19,25,27