Maximal -arcs in the projective plane of order 11

This work determines that the largest ( n , 4 ) -arcs in the projective plane of order 11, P G ( 2 , 11 ) , consist of 32 points. mber of classes of projectively equivalent complete and incomplete ( n , 3 ) -arcs in P G ( 2 , 11 ) is featured in the introduction. The full classification can be found in Coolsaet and Sticker (2012) [2]. assification of all ( n , 3 ) -arcs in P G ( 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 ) -arc. This search confirmed that in P G ( 2 , 11 ) no ( n , 3 ) -arc can be extended to a ( 33 , 4 ) -arc and that consequently m 4 ( 2 , 11 ) = 32 . ame algorithm is used to determine all four projectively inequivalent complete ( 32 , 4 ) -arcs that are extended from complete ( n , 3 ) -arcs.