  In the exploration of viable models of dynamical electroweak symmetry
breaking, it is essential to locate the lower end of the conformal window and
know the mass anomalous dimensions there for a variety of gauge theories. We
calculate, with the Schr\"odinger functional scheme, the running coupling
constant and the mass anomalous dimension of SU(2) gauge theory with six
massless Dirac fermions in the fundamental representation. The calculations are
performed on $6^4$ - $24^4$ lattices over a wide range of lattice bare
couplings to take the continuum limit. The discretization errors for both
quantities are removed perturbatively. We find that the running slows down and
comes to a stop at $0.06 \lesssim 1/g^2 \lesssim 0.15$ where the mass anomalous
dimension is estimated to be $0.26 \lesssim \gamma^*_m \lesssim 0.74$.
