Elias has T bags, each of which contains 4 numbered balls, with bag 'i' having balls numbered for each 'i'. Elias chooses one of the bags and then arranges the 4 balls into a row. Elias notices that there are strictly fewer than 1000 different arrangements of balls he could have seen. What is the largest possible value of T?

Details and assumptions
As an explicit example, if Elias has 3 bags, then bag 1 has balls labelled 1, 2, 3, 4, bag 2 has balls labelled 5, 6, 7, 8 and bag 3 has balls labelled 9, 10, 11, 12.

Question

Elias has T bags, each of which contains 4 numbered balls, with bag 'i' having balls numbered  for each 'i'. Elias chooses one of the bags and then arranges the 4 balls into a row. Elias notices that there are strictly fewer than 1000 different arrangements of balls he could have seen. What is the largest possible value of T?

Details and assumptions
As an explicit example, if Elias has 3 bags, then bag 1 has balls labelled 1, 2, 3, 4, bag 2 has balls labelled 5, 6, 7, 8 and bag 3 has balls labelled 9, 10, 11, 12.