Partitioning

[Michael]

Imagine a Lotto game with 20 balls, six are drawn.
How many and which tickets must we hold to
guarantee a Match 3?

By partitioning the 20 into {1 to 8 } {9 to 16} & {17 to 20}
The balls can only fall into their respective partitions by a
2-2-2- split or at least one partion having 3 balls in it.
We can arrive at, almost by inspection, the following cover.

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

09,10,11,12,13,14
09,10,11,12,15,16
09,10,13,14,15,16
11,12,13,14,15,16

01,02,17,18,19,20
03,04,17,18,19,20
05,06,17,18,19,20
07,08,17,18,19,20

So a match 3 can be guaranteed with just 12 tickets.
Can Tabu Search etc, working on the entire block of
20C6 draws match or better this cover? Is it always
better to attempt to solve these type of problems by
trying partitioning? Are there any rules that may be
applied that point to partitioning being inappropriate?
TIA Mick.