I don't know much about the theory but would like to learn a bit more. Does "subquadratic" mean that the ruler's length is less than the square of the number of marks? I suppose if one takes a ruler that is long enough, one can place 492114 internal marks on it in almost any integral positions, and it will be overwhelmingly likely that all the distances are distinct. About how long does the ruler have to be to make it easy to find Golomb rulers? On Thu, Oct 20, 2016 at 2:31 PM, Tomas Rokicki <rokicki@gmail.com> wrote:

I thought I would share that Gil Dogon and I, inspired by an Al Zimmermann programming contest, went ahead and calculated subquadratic Golomb rulers as reasonably far as we could. We were able to find subquadratic rulers through 492115 marks.

At 492116 marks, none of the known (to us) constructions led to a subquadratic ruler.

Is it possible that no subquadratic Golomb ruler exists at 492116 marks? Or is it more likely that one exists, and if so, is it something that we will ever explicitly know?

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