3if3 and 4if6 wheel in 65 lines

[BushHappy]

Here is a 3if3 100% and 4if6 100% wheel in 65 lines. Can anyone reduce the lines below 65 and maintain these guarantees?

1 2 3 4 6 17
1 2 3 8 11 12
1 2 4 6 8 16
1 2 5 7 8 9
1 2 5 8 9 10
1 2 7 8 14 15
1 2 8 11 13 19
1 2 8 12 17 18
1 3 4 5 9 12
1 3 6 10 13 16
1 3 6 11 16 17
1 3 6 14 15 18
1 3 7 10 18 19
1 4 5 13 14 17
1 4 7 9 10 17
1 4 11 15 16 18
1 4 12 14 16 19
1 5 6 9 14 19
1 5 7 9 15 16
1 5 9 11 13 18
1 6 7 10 12 15
1 7 10 11 13 14
1 12 13 15 17 19
2 3 4 9 17 18
2 3 5 12 15 19
2 3 6 10 12 14
2 3 7 13 15 16
2 4 5 6 13 18
2 4 7 11 12 18
2 4 8 14 15 18
2 4 10 16 18 19
2 5 7 8 9 10
2 5 11 14 16 17
2 6 7 14 17 19
2 6 9 11 15 19
2 9 12 13 14 16
2 10 11 13 15 17
3 4 5 7 14 16
3 4 5 10 11 15
3 4 6 7 8 19
3 4 8 10 12 13
3 5 6 9 13 17
3 5 8 12 16 18
3 7 9 11 12 17
3 8 9 14 15 17
3 9 10 16 17 19
3 11 13 14 18 19
4 5 8 11 17 19
4 6 9 10 11 14
4 6 12 15 16 17
4 7 9 13 15 19
4 8 9 11 13 16
5 6 7 11 12 13
5 6 8 13 14 15
5 6 10 13 16 19
5 7 15 17 18 19
5 10 12 14 17 18
6 7 9 14 16 18
6 8 9 12 18 19
6 8 10 11 17 18
7 8 11 12 14 15
7 8 13 16 17 18
7 10 11 12 16 19
8 10 14 15 16 19
9 10 12 13 15 18

Cheers,
BushHappy

 

[Brad]

CoverMaster wasn't able to reduce further, but have you considered relaxing the guarantee?

For example, a 99% cover will get CM(19,6,4,6)=50.

So by accepting just a 1% 4if6 'loss' in guarantee you could drop 15 lines from the wheel you posted. I ran a quick and dirty test but with a bit of patience CM may be able to go lower still.

Not sure what the record is for a full cover of your wheel but I think it won't be improved much, maybe 1 or 2 lines at best (I'm guessing).

 

[BushHappy]

Brad,

Here is another wheel with slighty reduced 4if6 cover:
64 Lines, 99.99263% 4if6 cover (2 Combinations not covered) and 100% 3if3 cover:

1 2 3 4 5 6
1 2 3 5 6 10
1 2 4 5 14 15
1 2 5 7 9 16
1 2 5 8 11 12
1 2 5 11 13 19
1 2 5 12 17 18
1 3 4 6 15 16
1 3 6 7 8 12
1 3 6 9 14 19
1 3 6 11 13 18
1 3 7 13 14 17
1 4 6 7 10 17
1 4 8 10 18 19
1 4 9 10 12 15
1 4 10 11 13 14
1 7 11 15 16 18
1 7 12 14 16 19
1 8 9 10 13 16
1 8 9 11 16 17
1 8 9 14 15 18
1 12 13 15 17 19
2 3 4 5 6 10
2 3 7 9 13 18
2 3 8 12 15 19
2 3 11 14 16 17
2 4 7 11 12 18
2 4 8 13 15 16
2 4 9 14 17 19
2 5 7 14 15 18
2 6 7 8 17 18
2 6 9 11 15 19
2 6 12 13 14 16
2 7 10 16 18 19
2 8 9 10 12 14
2 10 11 13 15 17
3 4 7 8 14 16
3 4 9 11 12 13
3 4 15 17 18 19
3 5 7 11 17 19
3 5 8 12 16 18
3 5 9 13 14 15
3 6 8 9 13 17
3 7 8 10 11 15
3 9 10 13 16 19
3 10 12 14 17 18
4 5 7 8 9 19
4 5 11 12 14 15
4 5 13 16 17 18
4 6 7 13 15 19
4 6 8 11 12 17
4 6 9 14 16 18
4 10 11 12 16 19
5 6 7 11 13 16
5 6 8 14 15 17
5 6 9 12 18 19
5 7 8 10 12 13
5 9 10 11 17 18
5 10 14 15 16 19
6 7 9 10 11 14
6 8 10 16 17 19
6 10 12 13 15 18
7 9 12 15 16 17
8 11 13 14 18 19

Cheers,
Vic