For character streams with 0 autocorrelation binary entropy is
<string_length>*log2(<character_set_size>). You
can check it with the ent command. Binary entropy of
128 is considered enough in the current climate. Notice
that doubling the character set's size only raises the entropy by 1.
E.g. base64 with all uppercase characters converted to
lowercase (around 38 characters) gives around 5.2 bits
compared to 6 bits of pure base64.
You can generate fairly secure (6 bits per character, 22 characters
to 128 bits) passwords with
cat /dev/urandom | base64 | head -c 22 | tr + = | tr '\n' -d.