Envelopes of \(k\)-arcs in projective planes over finite fields and Gröbner bases
This paper is a rich source of results concerning a method to calculate equations of algebraic envelopes associated to a \(k\)-arc in \(PG(2,q)\). It is based on Gröbner bases of ideals in \(GF(q) [x_0,x_1,x_2]\). This method is then applied to the complete 24-arc in \(PG(2,29)\) by \textit{J. M. Chao} and \textit{H. Kaneta} [Rend. Mat. Appl., VII. Ser. 16, No. 4, 537-544 (1996; Zbl 0879.51005)]. The details are too involved to be described here.
scientific article; zbMATH DE number 1279160