A problem to verify a lotto design

How can I do a program that verifies that lotto design L(39,7,4,7) is at most n by listing correct rows? Namely, I have to choose rows of seven numbers from the set 1,2,…,39 and I have to make sure that for any given extra row x1,x2,x3,x4,x5,x6,x7, at least one of those rows contain at least four correct numbers. I can use a checker that accept input of rows like

1 2 3 4 5 6 7
3 4 5 6 7 8 9

and then checks if those rows contains always at least four numbers given beforehand. I was wondering how good results one can find by computer.