New results for quasi-symmetric designs—An application of MACSYMA

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Abstract

Quasi-symmetric designs with block intersection numbers x and y are investigated. Let Γ be the usual block graph of such a design. Let c be the number of triangles on any edge of Γ, the complement of Γ. It is shown that for fixed values of x, y ⩾ 2 and c ⩾ 0 there are only finitely many such designs. This extends earlier results about quasi-symmetric designs with special properties. We show connections with strongly resolvable designs and also with designs considered by Holliday. The symbolic calculations were carried out using MACSYMA

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