Abstract
The following result is proved: Let D be a quasi-symmetric 3-design with intersection numbers x, y(0≤x<y<k). D has no three distinct blocks such that any two of them intersect in x points if and only if D is a Hadamard 3-design, or D has a parameter set (v, k, λ) where v=(λ+2)(λ2+4λ+2)+1, k=λ2+3λ+2 and λ=1,2,..., or D is a complement of one of these designs.
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Pawale, R.M. Quasi-symmetric 3-designs with triangle-free graph. Geom Dedicata 37, 205–210 (1991). https://doi.org/10.1007/BF00147414
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DOI: https://doi.org/10.1007/BF00147414