I somehow missed this back in 2008 or perhaps I saw they were not as
strong as carbon nanotubes in tensile strength so I didn't pay much
attention to them, but a team in 2008 announced development of what
they refer to as "colossal carbon tubes" which they say are stronger
than carbon nanotubes on a per weight basis:

Aug 8, 2008
Carbon nanotubes, but without the 'nano'.
http://physicsworld.com/cws/article/news/35364

Specific strength.
http://en.wikipedia.org/wiki/Specific_strength

Peng, H.; Chen, D.; et al., Huang J.Y. et al. (2008). "Strong and
Ductile Colossal Carbon Tubes with Walls of Rectangular Macropores".
Phys. Rev. Lett. 101 (14): 145501. doi:10.1103/PhysRevLett.101.145501
http://www.mse.ncsu.edu/research/zhu...T/PRL-CCTs.pdf [full
text]


The reason the team says the colossal carbon tubes have higher
specific strength than carbon nanotubes is because while their tensile
strength is 7 GPa, only slightly better than carbon composites long in
common use, their density is only 0.116 g/cm³(!)
These tubes so far are only centimeter lengths but another quite
useful aspect of them is their large diameters compared to nanotubes,
in the range of 50 to 100 microns. This is about the thickness of a
human hair. This would make them much easier to work with as far as
combining them together to create longer lengths.
If it is possible to join them and retain their individual strength
or make them at arbitrarily long lengths and retain the same strength
then they would be well in the range to make the space elevator
possible.


Bob Clark