Three new large (n, r) arcs in PG(2,31)

A set of n points in PG(2,q) some r of which are collinear, but every r+1 are not collinear, forms an (n, r) arc. By m_r(2, q) the maximum size of a such arc is denoted. In this talk (n, r) arcs with parameters (699, 24), (769, 26), and (838, 28) in PG(2,31) will be presented. The constructed arcs improve the respective lower bounds on m_r(2, 31) in [8]. As a consequence there exist three new three-dimensional linear codes over GF(31).