. Optimality A Golomb ruler of order m with length n may be optimal in either of two respects: It may be optimally dense, exhibiting maximal m for the specific value of n, It may be optimally short, exhibiting minimal n for the specific value of m. The general term optimal Golomb ruler is used to refer to the second type of optimality. Practical applications Information theory and error correction Golomb rulers are used within information theory related to error correcting codes. Radio frequency selection Golomb rulers are used in the selection of radio frequencies to reduce the effects of intermodulation interference with both terrestrial and extraterrestrial applications. Radio antenna placement Golomb rulers are used in the design of phased arrays of radio antennas. In radio astronomy one-dimensional synthesis arrays can have the antennas in a Golomb ruler configuration in order to obtain minimum redundancy of the Fourier component sampling. Current transformers Multi-ratio current transformers use Golomb rulers to place transformer tap points. Methods of construction A number of construction methods produce asymptotically optimal Golomb rulers. Erdős–Turán construction The following construction, due to Paul Erdős and Pál Turán, produces a Golomb ruler for every odd prime p. Known optimal Golomb rulers The following table contains all known optimal Golomb rulers, excluding those with marks in the reverse order. The first four are perfect. The optimal ruler would have been known before this date; this date represents that date when it was discovered to be optimal (because all other rulers were proved to not be smaller). For example, the ruler that turned out to be optimal for order 26 was recorded on , but it was not known to be optimal until all other possibilities were exhausted on . See also Costas array Volunteer computing BOINC distributed.net Perfect ruler Sidon sequence Sparse ruler References External links James B. Shearer's Golomb ruler pages distributed.net: Project OGR In Search Of The Optimal 20, 21 & 22 Mark Golomb Rulers Golomb rulers up to length of over 200 Antennas (radio) Distributed computing projects Length, distance, or range measuring devices Number theory