Hi @Thommy7571 : I've been sorta following this, and I'm afraid I'm a little confused (not unusual!).
Your OP is: "Which algorithm is used in JMP to create a random order of runs on the basis of a Seed for randomisation?"
So, it appears to me that you aren't asking about the design at all; you just want to know, once you have a design, how the runs are randomized. Is that correct?
If so, from an analysis point of view, it doesn't matter what the order of the runs is or what algorithm is used (so long as they are randomized such that each possible sequence of runs is equally likely). i.e., if you create a design with some random run order, then create the same design (same set of factor settings) with another random order, the designs are the same...run order doesn't enter in to it.
Apologies if I'm missing something.