  This work establishes the exact exponents for the soft-covering phenomenon of
a memoryless channel under the total variation metric when random (i.i.d. and
constant-composition) channel codes are used. The exponents, established
herein, are strict improvements in both directions on bounds found in the
literature. This complements the recent literature establishing the exact
exponents under the relative entropy metric; however, the proof techniques have
significant differences, and thus, neither result trivially implies the other.
  The found exponents imply new and improved bounds for various problems that
use soft-covering as their achievability argument, including new lower bounds
for the resolvability exponent and the secrecy exponent in the wiretap channel.
