Looking For An Optimized C(18,6,3,4)=25

[Rob Erhardt]

The current World Record(WR) cover for an 18-number
3 if 4 wheel is 25 tickets.

Has anyone noticed that Nicks version is somewhat
optimized for slightly better coverage?

My question is...can this be improved further...either in terms
of coverage or multiple hits?


Rob Erhardt

 

[Grandmaster]

<deleted>

 

[Rob Erhardt]

Oh, here is Nicks cover:

01 02 04 09 11 15
01 02 05 10 16 17
01 03 06 08 11 12
01 03 07 09 10 14
01 04 08 13 14 17
01 04 12 16 17 18
01 05 07 15 16 18
01 06 09

 

[Rob Erhardt]

Lets try that again:

Here is Nick`s design for 18,6,3,4,1=25

01 02 04 09 11 15
01 02 05 10 16 17
01 03 06 08 11 12
01 03 07 09 10 14
01 04 08 13 14 17
01 04 12 16 17 18
01 05 07 15 16 18
01 06 09 10 13 18
02 03 05 12 14 18
02 03 06 13 15 17
02 03 08 10 11 18
02 04 07 10 12 13
02 05 06 07 08 14
02 08 09 12 14 16
03 04 05 09 17 18
03 04 08 10 15 16
03 05 07 11 13 16
03 06 07 12 16 17
04 05 06 10 11 14
04 06 07 14 15 18
04 06 09 10 16 17
05 08 09 12 13 15
06 11 13 14 16 18
07 08 09 11 17 18
10 11 12 14 15 17

One might presume this is just a varient of Adolf Muel`s
WR listed at Peter`s web site.

It is NOT!!!

This is an entirely DIFFERENT wheel.

Careful analysis shows BETTER HIT RATIOS in all categories.

Maybe this IS the "most optimal" design.

I guess my question is...can it be improved even more?

Cheers,

Rob Erhardt