Tyler Cosgrove

Okay.

Because it's one unit distance, right?

Because it's not one... Yeah, it's not a unit distance.

Got it.

So then, OK, what's the next thing we can do?

The next kind of configuration is what's called the lattice construction.

And so if we can pull up a picture of it, it's this kind of crazy looking grid that has all these super intricate lines in between.

You can see it on the, this is from the OpenAI blog.

If we can pull it up here.

So this is what it looks like.

So if you can like zoom in on any of these points, you see that, you know, it looks like a grid, right?

But there's not just kind of pairs at the edges, right?

There's like way more.

Okay.

So this scales at n to the 1 plus 0, 1 over log log n, right?

This is basically the best kind of example that we know works.

We know we can find this, but is this the upper bound?

So this is basically the lower bound.

So then the question is like, we have the lower bound, which is that this is the best one we found.

This is the most number of pairs.