The complete arcs of PG(2,31)

We obtained a full computer classification of all complete arcs in the Desarguesian projective plane of order 31 using essentially the same methods as for earlier results for planes of smaller order, i.e., isomorph-free backtracking using canonical augmentation. We tabulate the resulting numbers of complete arcs according to size and automorphism group. We give explicit descriptions for all complete arcs with an automorphism group of size at least 20. In some of these cases the constructions can be generalized to other values of q. In particular, we find arcs of size 2 3 (q + 2) for any field of order q = 1 (mod 6), and a 44-arc in PG(2,67) with an automorphism group of order 88. We also correct a result by Kéri : there are 12 complete 22-arcs in PG(2,31) up to projective equivalence, and not 11.