Florida was supposed to begin the season Friday against Georgetown aboard the USS Bataan, but the game was canceled at halftime because there was moisture on the court.
The Gators led Alabama State 47-9 at halftime, the fewest points Florida has allowed in the first half since the implementation of the shot clock.
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Boynton shot 8 of 10 and made all four of his 3-point tries. He also had six rebounds and five assists.
Backup guard Bobby Brown led Alabama State (0-2) with 14 points.
Florida took an 8-0 lead and was ahead by 32 points with 6:24 left in the first half.
Patric Young had 12 points, 12 rebounds and two blocked shots for the Gators. Erik Murphy added 15 points and Mike Rosario had 14.
The Hornets missed 19 of their first 20 shots and went 2 for 25 overall in the first half. They finished 10 of 53 from the field and committed 19 turnovers.
The Gators played without junior Scottie Wilbekin, who was expected to be the starting point guard this season but is indefinitely suspended because of an undisclosed disciplinary issue. Forward Casey Prather, another potential starter, was out with a concussion.