Bounds on (n,r)-arcs and their application to linear codes

This article reviews some of the principal and recently-discovered lower and upper bounds on the maximum size of (n,r)-arcs in PG(2,q), sets of n points with at most r points on a line. Some of the upper bounds are used to improve the Griesmer bound for linear codes in certain cases. Also, a table is included showing the current best upper and lower bounds for q⩽19, and a number of open problems are discussed.