Near optimal Golomb rulers

This is an extension of a table by James B. Shearer. It shows the number of distinct optimal and near optimal Golomb Rulers with n marks.

The first column denotes the number of marks, n, the second column displays the length of the shortest rule, k, and the remaining columns show the number of distinct rulers with n marks and length k+0, k+1, k+2, etc.
When you follow a link you will find the list of the rulers that make up the entry. Note that the linked lists include all mirror rulers, thus the amount of rulers you will find is twice the number you see here.

n
k
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
3
1
1
2
2
3
3
4
4
5
5
6
6
7
7
8
8
9
9
10
10
11
11
12
12
13
13
14
14
15
15
16
16
17
4
6
1
3
4
9
8
15
17
24
24
36
36
48
49
63
64
81
80
99
101
120
120
144
144
168
169
195
196
225
224
255
257
288
288
5
11
2
7
14
21
38
50
80
95
142
158
240
245
346
381
490
514
700
716
910
940
1182
1222
1528
1528
1870
1949
2310
2337
2832
2850
3360
3415
3986
6
17
4
4
20
35
86
101
203
282
419
520
861
1007
1442
1622
2312
2633
3626
3865
5158
5805
7397
7862
10337
10856
13704
14495
18027
19043
23536
24188
29689
31271
37282
7
25
5
7
20
60
147
190
429
655
1048
1400
2305
3014
4618
5518
8359
9901
14187
16190
22724
26140
35559
38997
52598
59210
76267
82259
108929
117523
148679
160353
199597
216378
270378
8
34
1
9
14
48
91
192
379
763
1102
2155
3194
5281
7202
11552
15314
23052
28876
43038
53812
76454
91137
125713
152571
207023
237707
321495
370449
486564
546975
721296
808925
1026083
1138979
9
44
1
4
4
21
40
96
167
398
699
1425
2097
4101
6094
10423
14551
24434
33204
52330
68791
105890
136778
199772
246891
359357
448222
625208
747885
1039476
1251035
1677087
1964737
2632035
3077353
10
55
1
0
0
1
2
14
31
74
189
357
660
1159
2224
3696
6681
10306
17924
27062
44011
62046
101360
137989
210625
279484
425174
557424
827708
1034911
1498366
1865041
2637004
3233218
4508361
11
72
2
0
11
12
40
69
110
258
526
1064
1780
3404
5524
10387
16214
27770
41745
68634
102555
159546
227612
357487
489090
747516
1008317
1483472
1950893
2874753
3716407
5287110
6728721
9456371
11893348
12
85
1
0
0
0
0
1
5
9
23
41
107
208
372
759
1498
2487
4779
7765
14051
21511
37226
57040
94323
140717
225673
323491
512858
709497
1094225
1503118
2262643
3044549
4522366
13
106
1
0
0
3
3
9
21
28
72
147
277
564
989
1900
3094
5763
9194
16248
25678
43800
66374
110192
164396
265312
387241
610290
863662
1334752
1864878
2847518
3880399
5781503
7775078
14
127
1
1
3
1
6
4
10
26
45
96
188
309
651
1099
1963
3327
5944
9572
16868
26048
43609
67045
110306
165023
264965
385751
614417
873331
1360677
1914902
2920443
4048850
6088016
15
151
1
2
2
0
5
7
12
16
49
100
181
319
599
1026
1745
2980
5188
8145
13968
21794
36614
55345
91254
136641
219558
321815
508765
733842
1141168
1624314
2481160
3465920
5231327
16
177
1
1
3
3
6
7
18
21
44
82
149
253
458
739
1240
2124
3641
5753
10006
15386
24976
38827
62974
93539
150742
221435
349663
506559
788334
1125124
1726467
2431036
3675651
17
199
1
0
2
1
1
0
2
1
3
1
6
6
9
17
40
53
87
185
303
417
809
1299
2212
3373
5577
8780
14763
21953
35487
53620
85175
125486
196682


n
k
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
18
216
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
4
3
2
1
2
3
9
17
19
32
51
113
124
242
401
656
1058
1683
2762
4279
6975
10406
16802
25069
39428
58438
90823
132752
204326
297366




19
246
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
1
2
2
0
0
2
0
3
5
3
5
5
10
18
46
73
84
185
263
415
647
1112
1578
2647
3963
6302
9559
14784
22110
34197
49868
76972
111066
169746
242800
20
283
1
0
2
0
0
0
0
3
0
1
1
1
2
1
0
0
1
0
0
0
1
3
0
2
2
0
5
4
5
12
15
27
53




















21
333
1




















































22
356





















































23
372





















































24
425
1




















































25
480
1




















































26
492
1























































History:

Jun 22, 2009 - Added nogr21+0
Mar 18, 2009 - Didier Levet independently calculates nogr20+32 (This confirms nogr20+13)
Mar 02, 2009 - Added nogr26+0 according to official distributed.net results
Feb 12, 2009 - Apparently distributed.net did search the full nogr24+0, not just smaller rulers
Dec 30, 2008 - Added nogr25+0 according to official distributed.net results
Dec 28, 2008 - Didier Levet independently calculates nogr19+52 and uncovers some accounting errors in the listed nogr19+48 numbers (fixed after a recount)
Jul 30, 2007 - Didier Levet independently confirms nogr18+48
Jan 23, 2005 - Confirmed nogr19+32 and added nogr19+48 (This implicitly reveals nogr20+13)
Jun 17, 2004 - Confirmed nogr18+29 and added nogr18+48 (This implicitly confirms nogr19+20)
Jan 26, 2004 - Confirmed nogr17+14 and added nogr17+32 (This implicitly confirms nogr18+17)
Dec 21, 2003 - Confirmed nogr16+8 and added nogr16+32 (This implicitly confirms nogr17+12)
Dec 02, 2003 - Confirmed nogr15+16 and added nogr15+32 (This implicitly confirms nogr16+8)
Nov 13, 2003 - Confirmed and added new results up to and including nogr14+32 (Thanks to Didier Levet for notifying me about a bug)
Sep 20, 2003 - Created this page based on previous computations