The US Military is testing a small nuclear bomb...

...but without a nuclear bomb. They simply use 700 tons of explosives and try to hide it as a conventional bomb test. As far as I know, no airplane is capable to carry a 700 ton bomb.

And all the funny code names that the Defense Threat Reduction Agency (DTRA) uses:

In addition to Divine Strake, the DTRA has conducted or is planning to conduct, I've now learned, tests and experiments called Divine Buffalo, Divine Invader, Divine Helcat, Divine Kingfisher, Divine Umpire, Divine Zorro, Divine Warhawk, Divine Albatross, and my favorite Divine Hates, a test, according to DTRA documents, that will gauge "WMD production and storage tunnel complex functional defeat."

Early Warning by William M. Arkin - washingtonpost.com