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I believe that all of the cases are now known. See table 22 in http://arxiv.org/abs/1005.3750



Thanks for the link! That is pretty cool. I hadn't really thought about these kinds of questions, although operationally I can imagine applications for this, if you imagine columns and rows as redundant network links, and 'colors' being network services, you can prove that all your services have x4 redundancy this way. (I look at 16 x 16 grids all the time except they are 16 racks each with 16 servers :-)




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