Fano plane concept applied to lottery combinatorics

[coolcat]

I came across an interesting combinatorics optimisation description for 14numbers.
Maybe someone good in combinatorics can expand this fano plane concept to a full 45 numbers lottery design. Any suggestions?
http://en.wikipedia.org/wiki/Transylvania_lottery
http://mathworld.wolfram.com/FanoPlane.html

[Dason]

Are you still assuming you win if you get 2 out of 3 chosen?

[coolcat]

Are you still assuming you win if you get 2 out of 3 chosen?

Yes, if the 14combos from fano plane given in that link is correct.
(1) find an optimal way to overlap different sets of 14 numbers to form 2 sets X 3combos =6numbers, without duplicating exactly any of 6numbers.

(2) Expand the link's limited 14numbers fano plane method from scretch to cover N, numbers.

Any idea how to go about (1) or (2)?