What does 'put over' mean in this context?

Hi everybody,

I am reading a book in English and there is a phrasal verb--'put over'--that confuses me. Below is the paragraph containing the verb:

Last week the 20th Air Force ... put over the biggest bombing raid in
history, with 6,000 tons of bombs (about 3,000 tons of high explosives).
Today, the lead plane in our formation dropped a single bomb which
probably exploded with the force of 15,000 tons of high explosive. That
means that the days of large bombing raids, with several hundred planes,
are finished. A single plane disguised as a friendly transport can now wipe
out a city... (Dark Sun: The making of the hydrogen bomb)

I have consulted some dictionaries and basically they all agree that 'put over' has two meaning:
i. communicate successfully (= get across); and
ii. hold back to a later time (= postpone)

The problem is that, in my opinion, even though the 2nd meaning makes more sense, the 1st meaning can still fit in with the context, so I don't know which meaning I should interpret 'put over' as.

Can someone help me please?

Thank you very much in advance.
Yours sincerely.