  Applying the techniques developed in [AGG], we construct new real hyperbolic
manifolds whose underlying topology is that of a disc bundle over a closed
orientable surface. By the Gromov-Lawson-Thurston conjecture [GLT], such
bundles $M\to S$ should satisfy the inequality $|eM/\chi S|\leqslant1$, where
$eM$ stands for the Euler number of the bundle and $\chi S$, for the Euler
characteristic of the surface. In this paper, we construct new examples that
provide a maximal value of $|eM/\chi S|=\frac35$ among all known examples. The
former maximum, belonging to Feng Luo [Luo], was $|eM/\chi S|=\frac12$.
