Generate a table that meet conditions

I would like for an activity to generate a table that meet certain conditions as know as:

• There are 16 groups
• There are 8 activities
• Every group need to do every activity
• Each activity must accommodate 2 group and no more
• We would like a group to never meet the same group again (so the people can see the maximum amount of other people :-) )

We tried to manually generate this in Excel but there are always some groups that see each other again.

We tried to manually "generate a list" but we always end we teams crossing each other, like team 7 and team 9 cross 3 time in this exemple : table generated so far

I though maybe a thre dimensional array could do , but it seems like an overkill to me and there is certainly some known way to handle those situations.