Improved lower bounds on mr(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 mr(2,q). In this paper we finish our research on new (n,r)-arcs in PG(2,29), started in [Daskalov R., and E.Metodieva, New good (n, r)-arcs in PG(2, 29), in Proc. of Seventh International Workshop on Optimal Codes and Related Topics, 6-12 September 2013, Albena, Bulgaria, (2013), 79-84], and present six new large (n,r)-arcs with parameters (531, 20), (593, 22), (626, 23), (662, 24), (694, 25), and (725, 26). The constructed arcs improve the respective lower bounds on mr(2,29) in [Kohnert A., Arcs in the projective planes, Online tables, www.algorithm.uni-bayreuth.de/en/research/Coding_Theory/PG_arc_table/index.html].