Those numbers sound wild. For various comms systems does this mean several orders of magnitude bandwidth improvement or power reduction?
So it's only helpful for naturally high dimensional objects. Digital objects do not have a natural dimension (byte length), so you can choose a small dimension.
Due to the added variable aka axis, you have increased the size of complexity.
2d shapes packed in a 2d boundary vs 3d objects in 3d space. The difference is fitting quarters on a paper vs marbles in a perfect cube.
Now imagine having to find the most optimal method of packing for objects of Nth degree in Nth constraint. For example packing object that have 256 dimensional or variables into a constraint that also is 256 of complexity.
I feel as your dimension aka variable increases....the amount of information to compute grows quite quickly.
We can rule out some things as non optimal or non perfect, but we can also get close to perfection via trial and error. I see this as an example of the traveling salesman issue.
Do you stick with a randomly selected answer, do you go with the current most optimal solution, or do you invest time and effort into finding a new solution but you risk finding a worse solution. At the end of the day is the packing efficient gains worth the computational complexity of N dimension of N constraint given it will take an unknown amount of time to find a more efficient packing solution, and the new solution could be anywhere from 0.1% to 80% more efficient.