, Volume 2, Issue 2, pp 189-206

Quasi-symmetric designs and the Smith Normal Form

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Abstract

We obtain necessary conditions for the existence of a 2 − (ν, k, λ) design, for which the block intersection sizes s 1, s 2, ..., s n satisfy s 1s 2 ≡ ... ≡ s ns (mod p e ),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.

Communicated by V.D. Tonchev