Size of attachment and size of message
 

What's the maximum size of message that contains just a 100Mb attachment?

I've seen 138Mb but I presume there is an actual hard limit to the value, given the deterministic nature of the MIME encoding.

I guess you meant 138MB, since it seems no present email system I know of handles messages more then a few hundreds MB in size.
I the encoding is BASE64 then the encoded attachment is supposed to be 4/3 the size of the original, that is a bit more than 33% larger, but since it is broken into lines there's a bit extra for each line, and there's also the message body and headers, so that may account for the extra 4%.
But MIME also has the quoted-printable encoding, that may be much more wasteful: non-ASCII characters become at least 3 octets, that is a 200% increase in size. If the implementation takes a non western European encoding and maps it into utf-8 and then encodes it using quoted-printable encoding it may result in some characters being represented using 7 octets.


So it can become very inefficient. However this is nothing compared to what I observed about a decade or two ago with MS Outlook encoding of Hebrew test: it averaged in about 50 times the size of the original plain text (Outlook first applied explicit formatting to each word separately, instead of applying the formatting once to a paragraph or the complete body of the email, or not applying formatting at all when the composer of the message resorted to the default formatting, that is haven't chosen any formatting explicitly, and then applied an inefficient encoding to the result).