Energy levels, radiative transition wavelengths and probabilities have been studied for the W$^{26+}$ ion using multiconfiguration Dirac-Fock and Dirac-Fock-Slater methods. Corona and collisional-radiative models have been applied to determine lines and corresponding configurations in a low-density electron beam ion trap (EBIT) plasma. Correlation effects for the $4f^{2}$, $4d^{9}4f^{3}$, $4f5l$ ($l=0,...,4$), $4fng$ ($n=5, 6, 7$) configurations have been estimated by presenting configuration interaction strengths. It was determined that correlation effects are important for the $4f5s rightarrow 4f^{2}$ transitions corresponding to weak electric octupole transitions in a single-configuration approach. Correlation effects influence the $4f5d rightarrow 4f^{2}$ transitions by increasing transition probabilities by an order of magnitude. Identification of some lines observed in fusion plasma has been proposed. Spectra modeling shows strong increase of lines originating from the $4f5s rightarrow 4f^{2}$ transitions. Other transitions from the $10-30$ nm region can be of interest for the EBIT plasma.
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