Quasi-symmetric designs and the Smith Normal Form
We obtain necessary conditions for the existence of a 2 - (ν, k, λ) design, for which the block intersection sizes s1, s2, ..., snsatisfy s1 ≡ s2 ≡ ... ≡ sn ≡ s (mod pe),where p is a prime and the exponent e is odd. These conditions are obtained from restriction on the Smith Normal Form of the incidence matrix of the design. We also obtain restrictions on the action of the automorphism group of a 2 - (ν, k, λ) design on points and on blocks. © 1992 Kluwer Academic Publishers.
Blokhuis, A; Calderbank, AR
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