en عمومى General پژوهشي Research paper <p><span style="color: rgb(0, 0, 0); font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 11px; text-align: justify; background-color: rgb(243, 245, 246);">&nbsp;A</span>n $(n, r)$-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 &nbsp;PG(2, q) is denoted by $m_r(2,q)$. In this paper thirteen new $(n, r)$-arc in &nbsp;PG(2,,29) and a table with the best known lower and upper bounds on $m_r(2,29)$ are presented. The results are obtained by non-exhaustive local computer search.</p> Finite projective plane, $(n,r)$-Arc in a projective plane, $(l,t)$-Blocking set in a projective plane, Maximum size of an $(n,r)$-arc 127 138 http://ijmsi.ir/browse.php?a_code=A-10-2459-1&slc_lang=en&sid=1 R. Daskalov daskalovrn@gmail.com 10031947532846007812 10031947532846007812 Yes Department of Mathematics, Technical University of Gabrovo, Bulgaria. E. Metodieva metodieva56@gmail.com 10031947532846007813 10031947532846007813 No Department of Mathematics, Technical University of Gabrovo, Bulgaria.