I dont think that they were testing a large device, I think that they were testing a very small device, suitcase device if you will, that can be transported either by hand or in a small vehicle. Ponder that for a bit.
Even a nuke device as small as the one you mentioned would emit radiation in sufficient quantities to be easily detectable, and we haven't been able to detect any.
A nuclear device of that size is way beyond their capability. (And on a side note: Do you know how hard it is to start using the "L" key again after writing a sarcastic, I'm-so-ronery post?!) Larger devices allow for a sloppier implosion charge. If you can get some of the "pit" to compress enough to initiate the fission chain reaction, then the neutrons released will get most of the rest of the pit going as well. With a smaller pit, the margin for error goes way down. A slight imperfection will blow the pit apart rather than compressing it. This was either a fizzle or a fake.