After new questions and/or activities on older questions on "bounds for distances $2^S-3^N$" appeared in MO I thought whether a [BigList] or [CommunityWiki] on known such bounds (their references in literature and possibly their analytical derivations) would be helpful/meaningful/appropriate for MO.
I had a couple of weeks ago started the introduction for such a BigList, and, because it is much longer than to be useful for the body of this question, I give here only a link to the draft in the sandbox (Note, the given sandbox-link shall be operatable only a couple of weeks)
It contains, for motivation, two "classical" known bounds (G. Rhin and J. W. Ellison).
Moreover, I added one conjectural bound of mine, with a different basic characteristic of the formula but very nice fitting for $N$ up to 1 million digits. Perhaps this whole draft should thus be separated into 3 "answers" from the very start.
Remark after rereading my draft with this current question in mind: the intro/motivation should surely be rewritten/reorganized at all.
What do you think about starting such a [big-list]?