If you have browsed through the technical pages of Pierre Toscani, you
probably noticed he is quite knowledgeable when it comes to geometrical
optics. Although I cannot ascertain his schematics are correct, I
certainly trust him on this, as this is an extremely well researched
article.
Concerning the maximum possible lens aperture, Toscani says that since
the maximum angular aperture is about 54°, then the minimum f-number
is about 1.1. At least I can confirm this logic is sound: if you apply
the formula I derived in the linked thread, you get
1 / (2 sin(54°/2)) ≈ 1.10
If you use a tangent instead of a sine, you get 0.98 instead, which
shows that M. Toscani is fully aware that one should use a sine instead
of a tangent, since the second principal plane is actually a
sphere
(scroll down to the first figure).