Even though this was years ago, it is interesting so I wanted to take a stab at it. My interpretation, and the most “science” way, it would be designed would be a 3 stage thermonuclear bomb.
The (very) basics of how thermonuclear bombs work. A first stage (primary) fission bomb, a core of plutonium-239 or uranium-235 surrounded by a heavy metal tamper, is compressed through high explosives. Core reaches critical mass and fissions (started by a precisely timed neutron emitter).
As the primary fissions, it releases a massive amount of x-rays. These x-rays fill the space (radiation channel) between the primary and the secondary, which is a sphere or cylinder of a heavy metal tamper filled with hydrogen fuel (lithium deuteride) and a spark plug of U-235 or P-239 in the center. The outer weapons case, also a heavy metal, absorbs and reemits the x-rays. The weapons are designed so that the x-rays hit the secondary equally all around it, which causes it to compress, much like the high explosives did to the primary but with much more force. This causes the sparkplug to fission and bombards the hydrogen fuel, compressed between the expanding sparkplug and the compressing tamper, with neutrons, causing it to fusion (which is actually a complex series of fusions and fissions of lithium deuteride, where the lithium fissions from being hit by a neutron, creating helium, tritium, and energy. The created tritium then fusions with the deuterium, producing helium, a neutron, and energy, with the escaping neutron fissioning another lithium. Repeat).
These things happen very fast. All chain reactions happen in 0.0000005 seconds (half a microsecond), but 99.9% of the energy released comes from the last 7 out of 50-55 successive fission generations, which is about 0.00000007 seconds (0.07 microseconds). Being able to hold the compressed stage together infinitesimally longer will up the yield considerably. That is one of the reasons for the thick heavy metal tampers.
Finally, the secondary tamper and outer casing can add to the yield. If they are made from U-238, they will be induced to fission by the high-energy neutrons produced by the deuterium-tritium fusion reactions. About 50% of tested nuclear weapons final yield comes from this but it adds and insane amount of fallout. The Tsar Bomba was tested with the “clean” version, which replaced the U-238 with lead and had a yield of 50 megatons. The Soviets decided not to test the 100 megaton dirty version because it would have covered a significant portion of the Soviet Union if radioactive fallout. You can up the yield even more (possibly as much as 70% of total yield) by replacing U-238 with U-235 (the same as is used in the core of the primary).
The NOVA bomb is “nine fusion warheads encased in lithium triteride armor. When detonated, it compresses its fissionable material to neutron-star density, boosting the thermonuclear yield a hundredfold”. A fusion bomb is really a two stage thermonuclear bomb, where a fission primary is used to compress a mix of fusion/fission fuel enough to get largescale fusion. And we know that in modern weapons, as much as 70% of total yield can come from the final fission of U-235 tampers/case just by fusion neutron release (without compression).
So, I would arrange 9 two-stage thermonuclear weapons around a massive central “fusion” third-stage of U-235 and lithium deuteride. All 9 primaries would go off simultaneously (within a few billionths of a second), compressing and fusioning all 9 secondaries and simultaneously opening a radiation channel from each to the tertiary stage. Not only would the absolutely massive pressure be able to compress an absolutely massive tertiary, but neutron release would further fission everything as the weapon disassembled. If we were using 25 megaton secondaries, that is 225 megatons, meaning we could probably have a 250-300 megaton tertiary and a yield of over half a gigaton.
Ok. Now we can get into the fiction. The “lithium triteride armor” could be a fusionable case material made of lithium and tritium, like the fusion fuel lithium deuteride is made of lithium and deuterium. Maybe it is ultra-dense, ultra-strong, and fusions, which would boost each stage of this fictional weapon.
