The most logical, natural scrutable and downright useful would, not too surprisingly, be something like
Group of thirtytwo
Set of thirtytwo
.... or similar.
To construct a term based on rules which apply somewhat loosely at best to small sized groupings risks the result being essentially incomprehensible to the large majority of people.
While current accepted terms may appear to be systematically based this is not necessarily the case, and common usage may play a significant part. Historical accounts of the evolution of computing systems have reported that when IBM introduced 16 bit systems to its product line that they rejected "sexadecimal" and accepted "hexadecimal" as the term for 16 bit arithmetic because the inclusion of "sex" in the name was thought liable to 'cause problems'.
Names like duotrigectet are liable to be unfathomable to all but the most learned or pedantic. While some may be able to winkle out the meaning from the roots used most would get it wrong or lose interest.
If you have a well founded reason for needing or wanting a systematic nomenclature you should provide it so that people answering are able to address it more accurately.
Sexadecimal, Hexadecimal and IBM:
I suspect that at least in part "sexadecimal" wasn't chosen to avoid confusion with "sexagesimal". Do you have links for the historical accounts?
There are lots of such claims on the web. That's no proof, but much smoke suggests the possibility of fire. A few examples:
- Says: Note: As an interesting “sidebar”, the term hexadecimal was not the first one used for base-16 numbers in computing. Originally, these were called sexadecimal numbers. This is actually the correct term, since Latin prefixes (sexa-) are normally used for numbers, not Greek ones (hexa-). However, in the early 1950s, IBM decided that the word “sexadecimal” was just a little too “provocative” for their tastes, so they changed it to hexadecimal. IBM being IBM—especially back then—meant everyone else followed suit. As I understand it, neither term is etymologically perfect, but well, this note is long enough already. J
IBM story: http://daddybob.com/archives/qa060827.htm
In a book ...IBM ... - so must be true :-)
The story gets round
在20世纪50年代早期，IBM决定sexadecimal 有点太刺激，不对他们的口味，所以他们将其改为hexadecimal .IBM 就是IBM，特别是在那个时代，每个人都要服从IBM的规定。
aka: In the early 1950s, IBM decided sexadecimal little too exciting, not to their taste, so they changed it to hexadecimal .IBM is IBM, especially at that age, everyone must obey the provisions of IBM.