engleski

More quasi-symmetric 2-(56,16,6) designs

A t-(v, k, λ) design is a set of v points and a collection of k-subsets called blocks, with the property that any t-subset of points is contained in exactly λ blocks. The design is quasi-symmetric if any two blocks intersect either in x or in y points, for non-negative integers x < y. The existence of a quasi-symmetric 2-(56, 16, 6) design with intersection numbers x = 4 and y = 6 was established by V.D. Tonchev. The first design with these parameters was found as a residual design of a symmetric 2-(78, 22, 6) design. The second design was constructed by V.D. Tonchev and A. Munemasa, using the binary code spanned by the blocks of the known design. We construct hundreds of non-isomorphic quasi- symmetric designs with these parameters by assuming suitable automorphism groups.

quasi-symmetric designs

nije evidentirano