KritonK writes:
"On February 19, distributed.net began project OGR-28, the challenge to discover the Optimal Golomb Ruler with 28 marks. The previous challenge, OGR-27, is almost complete, with only 9 stubs remaining to be processed, as of February 19. People participating in that challenge do not need to update their client, as it can also process stubs for the new challenge."
(Score: 2, Informative) by KritonK on Thursday February 20 2014, @07:28PM
As soon as project OGR-27 is complete (any day now) the largest known optimal Golomb ruler will have 27 marks. Till then, the largest known optimal Golomb ruler has 26 marks.
Here [ibm.com] is a list of the shortest known Golomb rulers. The rulers of up to length 26 in that list are known to be optimal, the last three (24, 25, and 26) confirmed optimal by previous distributed.net projects. The OGR-27 project is expected to produce a shorter ruler than the one in the list. However, being pessimistic, I expect that it won't.
(Score: 1) by naubol on Friday February 21 2014, @04:02AM
How do they know, they tried every permutation of numbers up to the current shortest?
(Score: 1) by KritonK on Friday February 21 2014, @08:40AM
If you are asking how they know that rulers with length up to 26 are optimal, yes, they tried every possible permutation!
If you are asking how they know that the optimal ruler with length 27 is shorter than they shortest currently known, without having performed the brute force calculation, well, they don't. It's just a sense that they have. Those who understand the math might be able to explain why there is a high probability that the heuristically found ruler is not optimal. As for me, I'll stick to my pessimism.