Geodesic
On birational automorphisms of rational surfaces
Izvestiya. Mathematics , Tome 38 (1992) no. 2, pp. 251-275.

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Generators and relations of the groups of birational automorphisms are described for six classes of ($k$-minimal) rational surfaces. For surfaces $F$ with $\rho\colon=rk\operatorname{Pic}F=2$, $d\colon=K_F^2=3,4$ and $\rho=1$, $F(k)=\oslash$, $d=9$ relations between the already known generators are described, and for surfaces with $\rho=1$, $F(k)=\oslash$, $d=8,6$ and $\rho=2$, $F(k)=\oslash$, $d=8$ generators and relations are described. 
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V. A. Iskovskikh; S. L. Tregub. On birational automorphisms of rational surfaces. Izvestiya. Mathematics , Tome 38 (1992) no. 2, pp. 251-275. http://geodesic.mathdoc.fr/item/IM2_1992_38_2_a1/

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