We calculate a resummed equation of state with lattice QCD simulations at imaginary chemical potentials, generalizing the scheme introduced in our previous work to the case of non-zero $\mu_S$ , and focusing on the line of strangeness neutrality.
We present results up to $\mu_B/T\leq 3.5$ on the strangeness neutral line $\langle S\rangle=0$ in the temperature range 130~MeV$\leq T \leq $~280~MeV. We also extrapolate the finite baryon density equation of state to small non-zero values of the strangeness-to-baryon ratio $R=\langle S\rangle/\langle B\rangle $.
We perform a continuum extrapolation using lattice simulations of the 4stout-improved staggered action with 8, 10, 12 and 16 time slices. Finally we test the resummation scheme in a small volume by comparison with direct simulations.