Abstract
We show that a non-symmetric nearly triply regular \(2 - \left( {q^n ,q^{n - 1} ,\frac{{q^{n - 1} - 1}}{{q - 1}}} \right)\) designD with \(q^{n - 1} ,\nu 2 = q^{n - 3} \) and in which every line has at least q points is AG(n,q) for prime power q > 2 and positiveinteger n ≥ 3.
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Pascasio, A.A., Praeger, C.E. & Raposa, B.P. On the Characterisation of AG(n, q) by its Parameters asa Nearly Triply Regular Design. Designs, Codes and Cryptography 8, 173–179 (1996). https://doi.org/10.1023/A:1018045227727
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DOI: https://doi.org/10.1023/A:1018045227727