Perfect rulers (Rainer Rosenthal)

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Given m, find a complete ruler with m marks of largest possible length L R:{1,..,m}-->{0..L} strictly increasing , {R(j)-R(i),1<=i<j<=n}={1,..,L} A004137 http://www.luschny.de/math/rulers/ http://www.luschny.de/math/rulers/prulers.html http://www.luschny.de/math/rulers/optimalconjecture.html Think of a ruler with length L, where only m of its marks 0,1,2,...,L are visible. Let M be the set of these m visible marks. The ruler is called "perfect" if all differences up to L can be measured by the marks in M, i.e. if for every d not exceeding L there are two marks a and b in M with d = a - b. For given m find the largest L such that there is a perfect ruler of length L with m marks. Remark: For this type of rulers we demand the existence of at least one pair of marks for each difference. There is another kind of famous rulers, the so called Golomb rulers, where for each difference there is exactly one pair of marks, but not all differences have be measured.