Golomb ruler sequences

[Rainer Rosenthal]

> There are a few other scattered sequences related to 
> Golomb rulers that might be revisited as well.

There is a discussion in the german newsgroup de.sci.mathematik
scattered thru some threads since december 2002. It is related
to sequence A004137 and is concerned with Perfect Rulers:
http://mathworld.wolfram.com/PerfectRuler.html

We count the marks from 0 on up to length L. The Perfect Ruler
{0,1,4,6} has length L=6 and four marks.
The first interesting optimal Perfect Ruler has length L=13
and needs 6 marks only. 
Readers are kindly requested to become infected by the PR-virus.
So try to find out this (6,13)-Ruler. All the differences not
greater than 13 must be representable as m-m' with marks m and m'.
In the (4,6)-example above you easily verify that all 6 differences
can be measured: 1=1-0, 2=6-4, 3=4-1, 4=4-0, 5=6-1, 6=6-0.
It is NOT necessary to have exactly one representation for each
difference as in Golomb Rulers. 

For the interested reader I refer to two URLs, which Peter Luschny
and Klaus Nagel prepared during the discussion:
http://www.luschny.de/math/rulers/prulers.html
http://home.t-online.de/home/nagel.klaus/suddir/Suk.htm

Peter Luschny's computations showed errors in the old version
of A004137. Corrections have been made in the meantime and the old
version is now A080060.

Letting M be the number of marks and L the maximal length of a
Perfect Ruler of type (M,L), we know  M^2/L ~ 3 with infinitely
many M^2/L < 3. According to Leech one has M^2/L > 2.434.

Are there any new results regarding Perfect Rulers?

Thanks,
Rainer Rosenthal
r.rosenthal at web.de