Editing Golomb ruler (section)

==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 ruler|perfect]].

{| class="wikitable"
! Order !! Length !! Marks !! Proved{{ref label|unknown_index|*|^ *}} !! Proof discovered by
|-
| 1 || 0 || '''0''' || 1952<ref name="mathpuzzles">[http://mathpuzzle.com/MAA/30-Rulers%20and%20Arrays/mathgames_11_15_04.html Rulers, Arrays, and Gracefulness] Ed Pegg Jr. November 15, 2004. Math Games.</ref>|| Wallace Babcock
|-
| 2 || 1 || '''0 1''' || 1952<ref name="mathpuzzles" />|| Wallace Babcock
|-
| 3 || 3 || '''0 1 3''' || 1952<ref name="mathpuzzles" />|| Wallace Babcock
|-
| 4 || 6 || '''0 1 4 6''' || 1952<ref name="mathpuzzles" />|| Wallace Babcock
|-
| 5 || 11 || 0 1 4 9 11 <br /> 0 2 7 8 11 || c. 1967<ref name="shearer">{{cite web|url= http://www.research.ibm.com/people/s/shearer/grtab.html|archive-url=https://web.archive.org/web/20170625090514/http://www.research.ibm.com/people/s/shearer/grtab.html|archive-date=25 June 2017 |title= Table of lengths of shortest known Golomb rulers |last=Shearer|first=James B|date=19 February 1998| publisher= [[IBM]] }}</ref> || John P. Robinson and Arthur J. Bernstein
|-
| 6 || 17 || 0 1 4 10 12 17 <br /> 0 1 4 10 15 17 <br /> 0 1 8 11 13 17 <br /> 0 1 8 12 14 17 || c. 1967<ref name="shearer" /> || John P. Robinson and Arthur J. Bernstein
|-
| 7 || 25 || 0 1 4 10 18 23 25 <br /> 0 1 7 11 20 23 25 <br /> 0 1 11 16 19 23 25 <br /> 0 2 3 10 16 21 25 <br /> 0 2 7 13 21 22 25 || c. 1967<ref name="shearer" /> || John P. Robinson and Arthur J. Bernstein
|-
| 8 || 34 || 0 1 4 9 15 22 32 34 || 1972<ref name="shearer" /> || William Mixon
|-
| 9 || 44 || 0 1 5 12 25 27 35 41 44 || 1972<ref name="shearer" /> || William Mixon
|-
| 10 || 55 || 0 1 6 10 23 26 34 41 53 55 || 1972<ref name="shearer" /> || William Mixon
|-
| 11 || 72 || 0 1 4 13 28 33 47 54 64 70 72 <br /> 0 1 9 19 24 31 52 56 58 69 72 || 1972<ref name="shearer" /> || William Mixon
|-
| 12 || 85 || 0 2 6 24 29 40 43 55 68 75 76 85 || 1979<ref name="shearer" /> || John P. Robinson
|-
| 13 || 106 || 0 2 5 25 37 43 59 70 85 89 98 99 106 || 1981<ref name="shearer" /> || John P. Robinson
|-
| 14 || 127 || 0 4 6 20 35 52 59 77 78 86 89 99 122 127 || 1985<ref name="shearer" /> || James B. Shearer
|-
| 15 || 151 || 0 4 20 30 57 59 62 76 100 111 123 136 144 145 151 || 1985<ref name="shearer" /> || James B. Shearer
|-
| 16 || 177 || 0 1 4 11 26 32 56 68 76 115 117 134 150 163 168 177 || 1986<ref name="shearer" /> || James B. Shearer
|-
| 17 || 199 || 0 5 7 17 52 56 67 80 81 100 122 138 159 165 168 191 199 || 1993<ref name="shearer" /> || W. Olin Sibert
|-
| 18 || 216 || 0 2 10 22 53 56 82 83 89 98 130 148 153 167 188 192 205 216 || 1993<ref name="shearer" /> || W. Olin Sibert
|-
| 19 || 246 || 0 1 6 25 32 72 100 108 120 130 153 169 187 190 204 231 233 242 246 || 1994<ref name="shearer" /> || Apostolos Dollas, William T. Rankin and David McCracken
|-
| 20 || 283 || 0 1 8 11 68 77 94 116 121 156 158 179 194 208 212 228 240 253 259 283 || 1997?<ref name="shearer" /> || Mark Garry, David Vanderschel et al. (web project)
|-
| 21 || 333 || 0 2 24 56 77 82 83 95 129 144 179 186 195 255 265 285 293 296 310 329 333 || 8 May 1998<ref name="org2021">{{cite web |title= In Search Of The Optimal 20 & 21 Mark Golomb Rulers (archived)|date=26 November 1998 | publisher= Mark Garry, David Vanderschel, et al |url= http://members.aol.com/golomb20/index.html |archive-url=https://web.archive.org/web/19981206073704/http://members.aol.com/golomb20/index.html |archive-date=1998-12-06}}</ref> || Mark Garry, David Vanderschel et al. (web project)
|-
| 22 || 356 || 0 1 9 14 43 70 106 122 124 128 159 179 204 223 253 263 270 291 330 341 353 356 || 1999<ref name="shearer" /> || Mark Garry, David Vanderschel et al. (web project)
|-
| 23 || 372 || 0 3 7 17 61 66 91 99 114 159 171 199 200 226 235 246 277 316 329 348 350 366 372 || 1999<ref name="shearer" /> || Mark Garry, David Vanderschel et al. (web project)
|-
| 24 || 425 || 0 9 33 37 38 97 122 129 140 142 152 191 205 208 252 278 286 326 332 353 368 384 403 425 || {{date|13 October 2004}}<ref name="distributed.net OGR-24 completion announcement" /> || [[distributed.net]]
|-
| 25 || 480 || 0 12 29 39 72 91 146 157 160 161 166 191 207 214 258 290 316 354 372 394 396 431 459 467 480 || {{date|25 October 2008}}<ref name="distributed.net OGR-25 completion announcement" /> || [[distributed.net]]
|-
| 26 || 492 || 0 1 33 83 104 110 124 163 185 200 203 249 251 258 314 318 343 356 386 430 440 456 464 475 487 492 || {{date|24 February 2009}}<ref name="distributed.net OGR-26 completion announcement" /> || [[distributed.net]]
|-
| 27 || 553 || 0 3 15 41 66 95 97 106 142 152 220 221 225 242 295 330 338 354 382 388 402 415 486 504 523 546 553 || {{date|19 February 2014}}<ref name="distributed.net OGR-27 completion announcement" /> || [[distributed.net]]
|-
| 28 || 585 || 0 3 15 41 66 95 97 106 142 152 220 221 225 242 295 330 338 354 382 388 402 415 486 504 523 546 553 585 || {{date|23 November 2022}}<ref name="Completion of OGR-28 project" /> || [[distributed.net]]
|-
|}

{{note label|unknown_index|*|^ *}} <small>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 {{date|10 October 2007}}, but it was not known to be optimal until all other possibilities were exhausted on {{date|24 February 2009}}.</small>