The smallest possible bomb-like object would be a single critical mass of plutonium (or U-233) at maximum density under normal conditions. An
unreflected spherical alpha-phase critical mass of Pu-239 weighs 10.5 kg and is 10.1 cm across.
single critical mass cannot cause an explosion however since it does not cause fission multiplication, somewhat more than a critical mass is required
for that. But it does not take much more than a single critical mass to cause significant explosions. As little an excess as 10% (1.1 critical masses)
can produce explosions of 10-20 tons.
A mere 1.2 critical masses can produce explosive yield of 100 tons, and 1.35 critical masses can reach 250 tons. At this point a nation with
sophisticated weapons technology can employ fusion boosting to raise the yield well into the kiloton range without requiring additional fissile
material.
We can now try to estimated the absolute minimum possible mass for a bomb with a significant yield. Since the critical mass for alpha-phase plutonium
is 10.5 kg, and an additional 20-30% of mass is needed to make a significant explosion, this implies 13 kg or so. A thin beryllium reflector can
reduce this by a couple of kilograms, but the necessary high explosive, packaging, triggering system, etc. will add mass, so the true absolute minimum
probably lies in the range of 11-15 kg (and is probably closer to 15 than 11).
This is probably a fair description of the W-54 Davy Crockett warhead. This warhead was the lightest ever deployed by the US, with a minimum mass of
about 23 kg (it also came in heavier packages) and had yields ranging from 10 tons up to 1 Kt in various versions. The warhead was basically
egg-shaped with the minor axis of 27.3 cm and a major axis of 40 cm. The test devices for this design fired in Hardtack Phase II (shots Hamilton and
Humboldt on 15 October and 29 October 1958) weighed only 16 kg, impressively close to the minimum mass estimated above. These devices were 28 cm by 30
cm.
The W-54 nuclear package is certainly light enough by itself to be used in a "suitcase bomb" but the closest equivalent to such a device that US has
ever deployed was a man-carried version called the Mk-54 SADM (Small Atomic Demolition Munition). This used a version of the W-54, but the whole
package was much larger and heavier. It was a cylinder 40 cm by 60 cm, and weighed 68 kg (the actual warhead portion weighed only 27 kg). Although the
Mk-54 SADM has itself been called a "suitcase bomb" it is more like a "steamer trunk" bomb, especially considering its weight.
Compact nuclear artillery shells (208 mm and under) are based on a design approach called linear implosion. The linear implosion concept is that an
elongated (football shaped) lower density subcritical mass of material can be compressed and deformed into a critical higher density spherical
configuration by embedding it in a cylinder of explosives which are initiated at each end. As the detonation progresses from each direction towards
the middle, the fissile mass is squeezed into a supercritical shape. The Swift device is known to have been a linear implosion design.
A somewhat more sophisticated variation would extend the linear implosion concept to cylindrical implosion, in this case an oblate (squashed)
spheroid, roughly discus-shaped, of plutonium would be embedded in a cylinder of high explosive which is initiated simultaneously around its
perimeter. The cylindrically converging detonation would compress and deform the fissile mass into a sphere, that could be wider than the original
thickness of the system. This type of design would make the flattest possible bomb design, perhaps as little as 5 cm. The only obvious application for
such a device would be briefcase bomb, and would require a special development effort to create it.
They exist? Yes quite possibly.