Fano plane concept applied to lottery combinatorics

AI Thread Summary
The discussion focuses on applying the Fano plane concept to optimize lottery combinatorics, specifically for a 45-number lottery design. The main goal is to find a method to overlap different sets of 14 numbers to create six unique combinations of three numbers each, without any exact duplicates. Additionally, there is a request for strategies to expand the existing Fano plane coverage from 14 numbers to a larger set, denoted as N. Participants are encouraged to share ideas and methodologies for achieving these combinatorial challenges. The exploration aims to enhance lottery design through innovative mathematical approaches.
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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
 
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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)?
 

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