We provide classification results for translation generalized quadrangles of order less than or equal to 64, and hence, for all incidence geometries related to them. The results consist of the classification of all pseudo-ovals in \(\textrm{PG}(3n-1,2)\), for \(n=3,4\), and that of the pseudo-ovals in \(\textrm{PG}(3n-1,q)\), for \(n=5,6\), such that one of the associated projective planes is Desarguesian.

中文翻译：

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对伪椭圆、平移广义四边形和小阶兴隆拉盖尔平面进行分类

我们提供阶数小于或等于 64 的平移广义四边形的分类结果，因此也提供与它们相关的所有入射几何形状的分类结果。结果包括\(\textrm{PG}(3n-1,2)\)中所有伪椭圆的分类（对于\(n=3,4\) ）以及\(中伪椭圆的分类\textrm{PG}(3n-1,q)\)，对于\(n=5,6\)，使得关联的射影平面之一是笛沙格平面。