
handle: 11588/148272
\textit{T. Penttila} and \textit{B. Williams} [Geom. Dedicata, to appear] have constructed a sporadic translation ovoid of the quadrangle \(Q(4, 3^5)\). Associated with this, there is a new (semifield) flock of a quadratic cone in \(\text{PG}(3,3^5)\), and hence a flock generalized quadrangle of order \((3^5,3^{10})\). The authors prove that this generalized quadrangle is new. Moreover, it is a translation generalized quadrangle, and also its translation dual is shown to be new. The exciting news about this is that it provides a counterexample to a conjecture recently stated by \textit{J. A. Thas} [J. Comb. Theory, Ser. A 79, No. 2, 223-254 (1997; Zbl 0887.51004)], saying that every semifield flock generalized quadrangle is known (classical, Kantor or Ganley).
flocks, good eggs, generalized quadrangle, ovoids, Theoretical Computer Science, Computational Theory and Mathematics, flock, Discrete Mathematics and Combinatorics, egg, Generalized quadrangles and generalized polygons in finite geometry, translation generalized quadrangles
flocks, good eggs, generalized quadrangle, ovoids, Theoretical Computer Science, Computational Theory and Mathematics, flock, Discrete Mathematics and Combinatorics, egg, Generalized quadrangles and generalized polygons in finite geometry, translation generalized quadrangles
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