Geodesic
Classification of finite 3-nets of types I.3, I.4, I.5
Sbornik. Mathematics, Tome 186 (1995) no. 10, pp. 1429-1443

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Using the description of 2-transitive groups, in this paper finite 3-nets of types I.3, I.4, and I.5 are studied. According to the Barlotti-Strambach classification (see [4]) an arbitrary 3-net belongs to one of the seven Lenz classes I.1-I.5, II.1-II.2. In this work the question of the existence of nets of types I.3, I.4, I.5 remained open. The non-existence of a finite net of type I.5 is proved and the finite nets of type I.3 and I.4 are described up to isomorphism. 
@article{SM_1995_186_10_a2,
     author = {A. P. Il'inykh},
     title = {Classification of finite 3-nets of types {I.3,} {I.4,} {I.5}},
     journal = {Sbornik. Mathematics},
     pages = {1429--1443},
     publisher = {mathdoc},
     volume = {186},
     number = {10},
     year = {1995},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1995_186_10_a2/}
}
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A. P. Il'inykh. Classification of finite 3-nets of types I.3, I.4, I.5. Sbornik. Mathematics, Tome 186 (1995) no. 10, pp. 1429-1443. http://geodesic.mathdoc.fr/item/SM_1995_186_10_a2/