A two-dimensional family of surfaces of general type with p_g = 0 and K² = 7

We study the construction of complex minimal smooth surfaces S of general type with p_g(S)=0 and K_S²=7. Inoue constructed the first examples of such surfaces, which can be described as Galois Z/2Z×Z/2Z-covers over the four-nodal cubic surface. Later the first named author constructed more examples as Galois Z/2Z×Z/2Z-covers over certain six-nodal del Pezzo surfaces of degree one. In this paper we construct a two-dimensional family of minimal smooth surfaces of general type with p_g=0 and K²=7, as Galois Z/2Z×Z/2Z-covers of certain rational surfaces with Picard number three, with eight nodes and with two elliptic fibrations. This family is different from the previous ones.