Of course when DP=0 we can use symmetry everywhere easily. But at DP=5 or higher it's not the case and symmetry is not used in 3-way method.
DP=0 is not an interesting case in practic since you don't want to store all points.
Absolutely agree. But this was the starting point of many of my experiments to gradually increase DP while keeping "K" very low at the same time. I can't even explain some of the results to be honest, but they definitely only work when jumping through a symmetric interval; even when DP > 0 there are still a good number of collisions that wouldn't be expected to happen. So while it is still a mistery on why it works, it's definitely better than 1.7
Hoping to learn how you deal with cycles - I do not use any at all, I tried them, and stumbled pretty often even on very long length cycles. BTW, 2-cycles can be rendered impossible by having a strategic jump set via linear combinations checks.