  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
$3\sigma$ confidence level.
