  We calculate corrections to the BDS formula for the six-particle planar MHV
amplitude for the gluon transition 3->3 in the multi-Regge kinematics for the
physical region, in which the Regge pole ansatz is not valid. The remainder
function at two loops is obtained by an analytic continuation of the expression
derived by Goncharov, Spradlin, Vergu and Volovich to the kinematic region
described by the Mandelstam singularity exchange in the crossing channel. It
contains both the imaginary and real contributions being in agreement with the
BFKL predictions. The real part of the three loop expression is found from a
dispersion-like all-loop formula for the remainder function in the multi-Regge
kinematics derived by one of the authors. We also make a prediction for the
all-loop real part of the remainder function multiplied by the BDS phase, which
can be accessible through calculations in the regime of the strong coupling
constant.
