A solution for 8 persons on 21 occasions is as follows:--

1 8 6 3 4 5 2 7

1 8 4 5 7 2 3 6

1 8 2 7 3 6 4 5

The 1 is here a repeater, and the cycle 2, 3, 4, 5, 6, 7, 8. Every one

of the 3 groups will give 7 lines.