My high school is celebrating 30 years since graduating its first class and is planning to invite for lunch 20 alumni, 600 in all, from each of those classes. 

Hosts are planning to sit everyone in tables with the same number of alumni. They also wish to make sure that for any two classes, say years X and Y, at least one student from each of those two classes sit together in at least one of the tables.

For social distancing purposes, it is also desired to sit as few alumni as possible in each table.

How few can that be?