The SI unit of temperature will soon be redefined in terms of a fixed value of the Boltzmann constant k derived from an ensemble of measurements worldwide. We report on a new determination of k using acoustic thermometry of helium-4 gas in a 3 l volume quasi-spherical resonator. The method is based on the accurate determination of acoustic and microwave resonances to measure the speed of sound at different pressures. We find for the universal gas constant R = 8.314 4614(50) J.mol(-1).K-1. Using the current best available value of the Avogadro constant, we obtain k = 1.380 648 78(83) x 10(-23) J.K-1 with u(k)/k = 0.60 x 10(-6), where the uncertainty u is one standard uncertainty corresponding to a 68% confidence level. This value is consistent with our previous determinations and with that of the 2014 CODATA adjustment of the fundamental constants (Mohr et al 2016 Rev. Mod. Phys. 88 035009), within the standard uncertainties. We combined the present values of k and u(k) with earlier values that were measured at LNE. Assuming the maximum possible correlations between the measurements, (k(present)/< k> -1) = 0.07 x 10(-6) and the combined u(r)(k) is reduced to 0.56 x 10(-6). Assuming minimum correlations, (k(present)/< k> -1) = 0.10 x 10(-6) and the combined u(r)(k) is reduced to 0.48 x 10(-6).