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The best-known results for tiling rectangles in 2-D can be found here:
http://www2.stetson.edu/~efriedma/mathmagic/0299.htmlhttps://erich-friedman.github.io/mathmagic/0299.html
http://www2.stetson.edu/~efriedma/mathmagic/0299.html
https://erich-friedman.github.io/mathmagic/0299.html