However, on some of the other score lists, I only see maybe a dozen entries.
So, the problem must be:
Selecting the size of the board must be unclear to people. Since 4x4 is the "default", people play that level only.
People generally don't read the instructions before playing, so they would not necessarily know that other board sizes are available.
Any suggestions? Do I need a textbox on the screen to help out the user? Do I need buttons for each size?