engleski

On some recent results on biplanes and triplanes

The existence of a biplane with parameters (121, 16, 2) is an open problem. Recently, it has been proved by Alavi, Daneshkhah and Praeger that the order of an automorphism group of a possible biplane D of order 14 divide 2^7· 3^2· 5 · 7 · 11 · 13. We show that such a biplane do not have an automorphism of order 11 or 13. Further, we exclude a possible action of some small groups of order divisible by five or seven, on a biplane with parameters (121, 16, 2). Triplanes of order 12, i.e. symmetric (71, 15, 3) designs, have the greatest number of points among all known triplanes and it is not known if a triplane (v, k, 3) exists for v > 71. We give the first example of a triplane of order 12 that does not admit an automorphism of order 3, obtained by using binary linear codes.

biplane, triplane, automorphism group

nije evidentirano