Classification and construction of (k,3)‎-arcs on projective plane over Galois field GF(9)‎

الملخص EN

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.