Quasi-symmetric 2, 3, 4-designs

Sane, Sharad S. ; Shrikhande, Mohan S. (1987) Quasi-symmetric 2, 3, 4-designs Combinatorica, 7 (3). pp. 291-301. ISSN 0209-9683

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Official URL: http://www.springerlink.com/content/c20n0x1t162n17...

Related URL: http://dx.doi.org/10.1007/BF02579306


Quasi-symmetric designs are block designs with two block intersection numbers x and y It is shown that with the exception of (x, y)=(0, 1), for a fixed value of the block size k, there are finitely many such designs. Some finiteness results on block graphs are derived. For a quasi-symmetric 3-design with positive x and y, the intersection numbers are shown to be roots of a quadratic whose coefficients are polynomial functions of v, k and λ. Using this quadratic, various characterizations of the Witt-Luneburg design on 23 points are obtained. It is shown that if x=1, then a fixed value of λ determines at most finitely many such designs.

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