Maximal (n,4)(n,4)-arcs in the projective plane of order 11

This work determines that the largest (n,4)(n,4)-arcs in the projective plane of order 11, PG(2,11)PG(2,11), consist of 32 points.The number of classes of projectively equivalent complete and incomplete (n,3)(n,3)-arcs in PG(2,11)PG(2,11) is featured in the introduction. The full classification can be found in Coolsaet and Sticker (2012) [2].The classification of all (n,3)(n,3)-arcs in PG(2,11)PG(2,11) up to projective equivalence is the foundation of an exhaustive search that takes one element from every equivalence class and determines whether it can be extended to an (n′,4)(n′,4)-arc. This search confirmed that in PG(2,11)PG(2,11) no (n,3)(n,3)-arc can be extended to a (33,4)(33,4)-arc and that consequently m4(2,11)=32m4(2,11)=32.This same algorithm is used to determine all four projectively inequivalent complete (32,4)(32,4)-arcs that are extended from complete (n,3)(n,3)-arcs.