Fano plane concept applied to lottery combinatorics

[scalpmaster]

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

 

[scalpmaster]

Rephrasing the question,

(1) find a 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 coverage from scretch to N, numbers.

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