A new-generation x-ray laser project is explained. It is based on the transitions in Pd-like ions in nanoplasmas. The gain coefficient is calculated for the $4{d}_{3/2}^{9}5{d}_{3/2}[J=0]\ensuremath{-}4{d}_{3/2}^{9}5{p}_{1/2}[J=1]$ transition ($\ensuremath{\lambda}\ensuremath{\approx}10.8$ nm) in Pd-like tungsten. It is suggested that a cylindrical target made of nanostructured tungsten is pumped in the longitudinal direction by a laser pulse with energy 1--2 keV and duration $~500$ ps. For this pump pulse the target density and dimensions are calculated, as well as the temporal variations of the optimal plasma parameters for attaining $\mathit{gL}$ $~$ 14. The energy yield in the 10.8-nm line is more than ${10}^{20}$ eV.
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