In the new method we transpose the matrix describing the image elements. Instead of a 64x1024 matrix we now have a 1024x64 matrix. After this the rest is the same as the old method (but modified to work with this transposed system).
Some observations: The new algorithm works better at low N since the average value contains much more information (1024 elements vs. 64).
Also, while the new method seemes to perform better at low N, the importance here is the resulting size. The new method has a larger overhead because of the more information stored in the average array. Maybe a diagonal compare is more fair (with regards to filesize).
But first, we will compare the base (@ N=64) of the old and the new:
Old: (64 x 8x8 blocks, most significant to the right)
New: (64 x 32x32 blocks, most significant to the right)
| N | Old method | New method |
| 1 |  Size:1.78 kb |  Size:5.73 kb |
| 2 |  Size:2.71 kb |  Size:6.46 kb |
| 5 |  Size:5.02 kb |  Size:8.91 kb |
| 10 |  Size:8.32 kb |  Size:12.9 kb |
| 15 |  Size:11 kb |  Size:16.3 kb |
| 20 |  Size:13.4 kb |  Size:20.1 kb |
| 32 |  Size:18.4 kb |  Size:27.4 kb |
| 64 |  Size:28.1 kb |  Size:40.9 kb |
While it is possible to have up to N=1024 on the new method, it makes little sence. The size after this compression is 591 KB with little (no) percieved difference)