The generally accepted boundary between Earth’s atmosphere and “outer space” is most often demarcated by the “Kármán line” (after the Hungarian-American physicist and aeronautical engineer Theodore von Kármán), at an altitude of 100 kilometers (62 miles) above sea level. Other tests are considered merely “high altitude” or “near space.”
This list does not include failed shot attempts, but only those with confirmed nuclear detonations.
Of special note is the frantic pace of tests by both the US and USSR in October and early November 1962, coinciding with the approximate period of the Cuban Missile Crisis, which although not directly related, undoubtedly helped to ratchet up the level of international tension.