Since each participants will meet only 36 of the 99 other participants, there's plenty of room to set up a schedule.
One simple way is to divide the participants into four sets of 25, and arrange the tables (at least virtually) in a circle. In each round every table contains one person from each set.
Everyone in set 0 stay where they are for the entire event. Everyone in set 1 will move 1 table clockwise after each round. Everyone in set 2 will move 2 tables clockwise after each round. And everyone in set 3 moves 3 tables clockwise after each round.