The affine plane AG(2,q), q odd, has a unique one point extension.
Inventiones mathematicae, Tome 118 (1994) no. 1, pp. 133-140.

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Mots-clés : inversive plane, flocks
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     author = {J.A. Thas},
     title = {The affine plane {AG(2,q),} q odd, has a unique one point extension.},
     journal = {Inventiones mathematicae},
     pages = {133--140},
     publisher = {mathdoc},
     volume = {118},
     number = {1},
     year = {1994},
     zbl = {0814.51002},
     url = {http://geodesic.mathdoc.fr/item/IM_1994__118_1_144232/}
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J.A. Thas. The affine plane AG(2,q), q odd, has a unique one point extension.. Inventiones mathematicae, Tome 118 (1994) no. 1, pp. 133-140. http://geodesic.mathdoc.fr/item/IM_1994__118_1_144232/