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@HenryCohn Presumably, 4D printing is 3D printing with programable shape transformation (i.e., the time axis gives the 4th dimension) like this: ted.com/talks/…
This doesn't help you solve the problem, but I'm pretty sure the paper by "Wanless and Church" you mentioned is actually a single-authored paper. The supposed second author "Christ Church" isn't a person. It's a college in the University of Oxford the author was affiliated with.
@TheMaskedAvenger No perfect Golomb ruler of length larger than $6$ exists, though. So, essentially $\{0,1\}$, $\{0,1,3\}$, and $\{0,1,4,6\}$ are the only ones that meet the bound $\binom{\vert A\vert}{2} \geq N$ with equality. Completeness is required for OP's purpose.
