Singular

What is the largest n that GF(2^n) can support in Singular?

From 6.1 Limitations of Singular http://www.singular.uni-kl.de/Manual/la ... htm#SEC386 ,
"the number of elements in GF(p,n) must be less than 65536 " which means the "n" can at most be 16, is this correct?

But in my computation, I found "n" could be much larger. I am confused here. Could you please explain this?

Thanks
Gepo

That depends on the way the ring is defined.
For the form

the maximum for n is 15 (not 16: less than 2^16).
For the form

the maximal n is the maximal degree of the minpoly, which is
at least 65536.