Bounds on $m_r(2,29)$

 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 thirteen new $(n, r)$-arc in  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.