Larger diameter gives stronger coupling to space (lower Q, wider bandwidth), up to the point where the conductor fills half the space of the antenna itself (give or take), at which point, the negative space being cut off by the conductor reduces bandwidth again.
The widest bandwidth designs are self-similar, where the positive and negative space are equal, under the symmetry of the antenna. The type of symmetry defines the directivity and polarization: translational symmetry (similar along an axis) gives unidirectional response, rotational symmetry gives circular polarization, etc.
So, if you want a modest bandwidth, like, uh, probably 30 to 50%, for something about that size and dipole-like (I guess it's not a dipole, but perhaps a folded dipole, loop, rhombic or such; anything electrically resonant-sized), you're probably about there. But if you're going for wideband, like octaves or more, you'll want something bigger like a log periodic.
Tim
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