  In Part II we show that there exist quantum codes whose probability of
undetected error falls exponentially with the length of the code and derive
bounds on this exponent.The lower (existence) bound for stabilizer codes is
proved by a counting argument for classical self-orthogonal quaternary codes.
Upper bounds for any quantum codes are proved by linear programming. We present
two general solutions of the LP problem. Together they give an upper bound on
the exponent of undetected error. The upper and lower asymptotic bounds
coincide for a certain interval of code rates close to 1.
