Constructions of small complete arcs with prescribed symmetry.

Contributions to Discrete Mathematics 3 (2008), 14-19.

We use arcs found by Storme and van Maldeghem
in their classification of primitive arcs in PG(2,q)
as seeds for constructing small complete arcs in these planes.
Our complete arcs are obtained by taking the union of
such a ``seed arc'' with some orbits of a subgroup of its stabilizer.
Using this approach we construct
five different complete 15-arcs fixed by Z_{3} in PG(2,37),
a complete 20-arc fixed by S_{3} in PG(2,61),
and two different complete 22-arcs fixed by D_{5} in PG(2,71).
In all three cases, the size of complete arcs constructed
in this paper is strictly smaller than the size of the smallest
complete arcs (in the respective plane) known so far.