I tried to use set clip points to make the points not plot at the edges of the graph, but it wasn't working, so I just set the xrange and made the first and last points outside of the graph instead of right on the edges.
Then I converted the square.ps file to PDF, opened it in Adobe Illustrator, changed the fill style for the circles, changed the line style for the vertical lines, and saved.
Enter 500 under Resolution (it doesn't say "DPI" but I think that's what it means)
Uncheck Try bounding box (since the bounding box cuts off the edge, unfortunately. You can try with the bounding box first.)
Enter large values for Width and Height
Check Color
Check Strong anti-aliasing for both graphics and text
Crop off extra whitespace (Shift+C if you can't find it in the toolbox)
Possibly need to rotate it: Click Image → Transform → Rotate 90 degrees clockwise
Filters → Blur → Gaussian blur at 2.0 px (No need to blur if you use strong anti-aliasing during conversion. I see no significant difference between end results.)
Image → Scale Image...
Width and Height at 25%
Cubic interpolation
You can view at normal size if you want by pressing 1, Ctrl+E
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