Classification and Construction of (k,3)-Arcs on Projective Plane Over Galois Field GF(9) - Ahmad, Adil M.; Al-Mukhtar, Amaal SH.; Kareem, Fatima. F. (Ibn AL-Haitham Journal For Pure and Applied Sciences, 2017)
In this work, we construct and classify the projectively distinct (k,3)-arcs in PG(2,9), where k ≥ 5, and prove that the complete (k,3)-arcs do not exist, where 5 ≤ k ≤ 13. We found that the maximum complete (k,3)-arc in PG(2,q) is the (16,3)-arc and the minimum complete (k,3)-arc in PG(2,q) is the (14,3)-arc. Moreover, we found the complete (k,3)-arcs between them.