We present the current status of the BMV experiment. Our apparatus is based on an up-to-date resonant optical cavity coupled to a transverse magnetic field. We detail our data acquisition and analysis procedure which takes into account the symmetry properties of the raw data with respect to the orientation of the magnetic field and the sign of the cavity birefringence. The measurement result of the vacuum magnetic linear birefringence k_mathrm{CM}$ presented in this paper was obtained with about 200 magnetic pulses and a maximum field of 6.5,T, giving a noise floor of about $8 times 10^{-21}$,T$^{-2}$ at $3sigma$ confidence level.
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