The complete (k, 3)‐arcs of PG(2,q),q≤13
Kris Coolsaet, Heide Sticker · Journal of Combinatorial Designs · 2011
Abstract We have classified by computer the projectively distinct complete (k,3)‐arcs inPG(2,q),q≤13. The algorithm used is an application of isomorph‐free backtracking using canonical augmentation, an adaptation of our earlier algorithms for the generation of (k,2)‐arcs. We describe those parts of the algorithms which are specific to the particular problem of (k,3)‐arcs. For each of these arcs we have also determined the automorphism group. The results are summarized in tables where the arcs are listed according to size and automorphism group. For the arcs with the larger automorphism groups, explicit descriptions are given. Part of the computer results can be generalized to other values ofq: we describe constructions of arcs havingS4as a group of automorphisms, arcs containing the union of three “half conics” and arcs constructed from parts of cubic curves. Copyright © 2011 Wiley Periodicals, Inc. J Combin Designs 20:89‐111, 2012