Hello, I'm using cube explorer to find all the cases for my new method,

HVLS.

I tried to find out how to get all the possible cases by doing R U R' U' in cube explorer, removing all LL corners, besides the one from the removed F2L pair. I got 324 algorithms out of it, but I had somebody do the math and there should only be 162.

So my question is: Why is there 324 cases, instead of 162?

First of all, I'm sorry to say but that isn't a new method. What you described as HVLS is really WVCP (Winter Variation + Corner Permutation) and has been discussed before, I think algs have been created too.

But to (try to) answer your question however, it's not the math that's wrong but probably rather the way you were using Cube Exploror. On a video I watched a while ago, it says to do this to find all the possible cases for your input:

1) draw in the cube (you've already done that)

2) hit "Add and solve"

3) Wait. The video said at least until it gets to (21f) but that'll take a loonngg time probably, but for your purposes (16f) should be just fine.

4) Press "Stop Search" then "add solutions to main window"

5) then go to File>Save maneuvers and choose a file location

6) then go to options and check "Skip isomorphics when loading from file" AND "Isomorphy includes Inversion"

7) go to file>load maneuvers and find and select your file

8) Click "yes" when is asks about discarding cubes in the main window

9) you should have all the possible cases for the WVCP. They won't be the best algs but you'll have all the cases at least, to find better algs you'll have to search them one by one in cube explorer

If that didn't work then I don't know, that's what the guide I looked at said to do.