In order to win the super-jackpot, one must roll the exact lucky number 77.7777.
In order to win the Super-Jackpot, one must roll the exact lucky number 55.5555:
77.7777, 55.5555 or both

Decided to make it 55.5555 so that 77.7777 doesn't win two jackpots. Updated the OP to reflect this.