Luengo Velasco, IgnacioLópez, BartoloméChristensen, ChrisSundaram, GaneshSundaram, AvinashBajaj, Chandrajit2023-06-202023-06-2020043-540-00475-0https://hdl.handle.net/20.500.14352/53148Conference: Conference on Algebra, Arithmetic, Geometry and its Applications Location: Purdue Univ, W Lafayette, in Date: Jul 20-26, 2000We present a method to find curves over the finite field F-3 with many rational points. The method is based in an arithmetic study of linear systems of projective plane curves of a given degree and prescribed singularities. We have found curves of genera 4, 5, 6, 7 and 8 which in the cases of genera 5 and 8 improve the existent bounds for the number of rational points, and in the cases of genera 4, 6 and 7 reach these bounds.book partmetadata only access512CodesÁlgebra1201 Álgebra