Geodesic
The Hering plane and associated designs
Matematičeskie zametki, Tome 60 (1996) no. 6, pp. 873-881

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We associate an affine plane ${\mathscr A}_f$ with any automorphism $f$ of the additive group of the field $F=\operatorname{GF}(q)$, where $q$ is odd, $F^*=\Delta\cup-\Delta$, and $\Delta=\bigl\{x^fx\mid x\in F^*\bigr\}$. We compute the ternar of the plane ${\mathscr A}_f$. A simple construction of the Hering plane in the case $q=27$, $x^f=x-\operatorname{Tr}x=-x^3-x^9$ and two designs associated with it are described in detail. 
@article{MZM_1996_60_6_a8,
     author = {A. P. Il'inykh},
     title = {The {Hering} plane and associated designs},
     journal = {Matemati\v{c}eskie zametki},
     pages = {873--881},
     publisher = {mathdoc},
     volume = {60},
     number = {6},
     year = {1996},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1996_60_6_a8/}
}
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A. P. Il'inykh. The Hering plane and associated designs. Matematičeskie zametki, Tome 60 (1996) no. 6, pp. 873-881. http://geodesic.mathdoc.fr/item/MZM_1996_60_6_a8/