  We report on our on-going effort to measure the Boltzmann constant, kB, using
the Doppler Broadening Technique. The main systematic effects affecting the
measurement are discussed. A revised error budget is presented in which the
global uncertainty on systematic effects is reduced to 2.3 ppm. This
corresponds to a reduction of more than one order of magnitude compared to our
previous Boltzmann constant measurement. Means to reach a determination of kB
at the part per million accuracy level are outlined.
