Transitive A 6-invariant k-arcs in PG(2, q)

For q = p (r) with a prime p a parts per thousand yen 7 such that or 19 (mod 30), the desarguesian projective plane PG(2, q) of order q has a unique conjugacy class of projectivity groups isomorphic to the alternating group A (6) of degree 6. For a projectivity group of PG(2, q), we investigate the geometric properties of the (unique) I"-orbit of size 90 such that the 1-point stabilizer of I" in its action on is a cyclic group of order 4. Here lies either in PG(2, q) or in PG(2, q (2)) according as 3 is a square or a non-square element in GF(q). We show that if q a parts per thousand yen 349 and q not equal 421, then is a 90-arc, which turns out to be complete for q = 349, 409, 529, 601,661. Interestingly, is the smallest known complete arc in PG(2,601) and in PG(2,661). Computations are carried out by MAGMA.