Abstract
An (????,3)-arc ???? in projective plane ????????(2,????) of size ???? and degree three
is a set of n points such that every line in the plane meet it in less than
or equal three points, also the arc ???? is complete if it is not contained
in (????+1,3)-arc. In this paper, the classification of degree three arcs in
�
�????(2,19) is introduced in details according to their stabilizer groups.
The motivation for working in the projective plane of order 19 is
twofold. First, the size of the largest (????,3)-arc is not known. Second,
the number of (????,3)-arcs is significantly higher in the projective plane
of order 19 than it is in the projective plane of order ???? for ????<19,
giving a large number of (????,3)-arcs for the study.
is a set of n points such that every line in the plane meet it in less than
or equal three points, also the arc ???? is complete if it is not contained
in (????+1,3)-arc. In this paper, the classification of degree three arcs in
�
�????(2,19) is introduced in details according to their stabilizer groups.
The motivation for working in the projective plane of order 19 is
twofold. First, the size of the largest (????,3)-arc is not known. Second,
the number of (????,3)-arcs is significantly higher in the projective plane
of order 19 than it is in the projective plane of order ???? for ????<19,
giving a large number of (????,3)-arcs for the study.
Keywords
Projective Plane; Arcs ; Group action; Stabilizer Group