  We compute the ratio Lambda_L/Lambda_MS, where the scale parameter Lambda_L
is associated with a lattice formulation of QCD. We consider a 3-parameter
family of gluon actions, which are most frequently used for O(a) improvement a`
la Symanzik. The gluon action is put togeter with standard discretizations for
fermions (Wilson/clover, overlap), to provide Lambda_L for several possible
combinations of fermion and gluon actions. We employ the background field
technique in order to calculate the 1PI 2-point function of the background
field; this leads to the coupling constant renormalization function, Z_g, at
1-loop level.
  Our results are obtained for an extensive range of values for the Symanzik
coefficients.
