Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Serdica Journal of Computing, Vol. 1, No 3, (2007), 279p-292p
Two heuristic algorithms (M65 and M52) for finding respectively
unitals and maximal arcs in projective planes of order 16 are described.
The exact algorithms based on exhaustive search are impractical because of
the combinatorial explosion (huge number of combinations to be checked).
Algorithms M65 and M52 use unions of orbits of di erent subgroups of the
automorphism group of the 273x273 bipartite graph of the projective plane.
Two very efficient algorithms (developed by the author and not described
here) are used in M65 and M52: (i) algorithm VSEPARN for computing
the generators, orbits and order of the graph automorphism group; (ii)
graph isomorphism algorithm derived from VSEPARN. Four properties are
proved and used to speed up the algorithms M65 and M52. The results of
these algorithms are published. After changing only the parameters of these
algorithms they can be used for determining unitals in projective planes of
The paper has been presented at the International Conference Pioneers of Bulgarian
Mathematics, Dedicated to Nikola Obreshkoff and Lubomir Tschakalo ff , Sofia, July, 2006.