dknowles67 wrote:That is to say, a 1 round PPN chart is the first round of a PN chart using a set of keys different from the ones published on your web-page, in order to obtain "more interesting charts"?
This might be true but it's probably not the best way to characterize PPN, i.e. as being pieces of PN. I would conjecture that any Lane Rotation chart is part of a PN chart, in most cases a really big PN chart. And most Lane Rotation charts are not PPN.
IMO, it is more accurate to think of PN as a special case of PPN, where the matchup count spread is 0 instead of 1.
Another good way to think of PPN is as "smart" Lane Rotation.
Here's a "dumb" Lane Rotation chart, 7 cars, 4 lanes, 1 round.
1 2 3 4
2 3 4 5
3 4 5 6
4 5 6 7
5 6 7 1
6 7 1 2
7 1 2 3
It satisfies lane equity, but not opponent equity. For example, Car 1 races Car 2 three times, but Car 1 only races Car 5 one time, so it's not PPN
It's a "dumb" chart because the first race is poorly chosen, 1-2-3-4.
Here's a "smart" Lane Rotation chart:
1 3 5 2
2 4 6 3
3 5 7 4
4 6 1 5
5 7 2 6
6 1 3 7
7 2 4 1
This chart has a good first race, 1-3-5-2. It's a good first race because the resulting chart is PPN. And because the dimensions happen to work out just right, it's also PN.
This way of looking at things is where PPN came from.
Historically -- in the PWD community, at least -- PN came first, then CPN, then PPN. Logically, however, the order is different -- all CPN charts are PN, and all PN charts are PPN.
The way the information is displayed on the web sites does reflect the historical aspect, and admittedly this probably makes it all a little harder to digest.
One of the hard parts of all this is finding keys/generators/patterns or whatever you want to call them, for new combinations of cars, lanes, and rounds.
Stan and I do not have a quick and clean way to find them. We have to hunt them down ahead of time and then statically encode them into ppngen.html and ppn.dll.
