Abstract
Quasi-symmetric designs (QSDs) with particular block graphs are investigated. We rule out the possibility of a QSD with block graph that has the same parameters as that of the Symplectic graph Sp(2t, q), where q is an odd prime power or its complement. We obtain support for Bagchi’s recent conjecture, which states that ‘For the existence of a quasi-symmetric 2-design with block graph \(K_{m\times n}\), we must have \(m \equiv n+ 1 \pmod {n^2}\)’. Under certain conditions, we rule out the possibility of a QSD having a pseudo-Latin square or negative Latin square block graph.
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The authors would like to thank the anonymous referee for suggesting improvements on the earlier stated results.
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Communicated by K. T. Arasu.
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Pawale, R.M., Shrikhande, M.S. & Rajbhar, K.S. Non-existence of quasi-symmetric designs with restricted block graphs. Des. Codes Cryptogr. 90, 871–879 (2022). https://doi.org/10.1007/s10623-022-01016-4
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DOI: https://doi.org/10.1007/s10623-022-01016-4