This web page contains a table giving the lengths of the shortest known Golomb rulers for up to 150 marks. The values for 23 marks or less are known to be optimal. For the actual rulers see
marks | length | found | by | proved | by | comments |
---|---|---|---|---|---|---|
1 | 0 | trivial | ||||
2 | 1 | trivial | ||||
3 | 3 | trivial | ||||
4 | 6 | trivial | ||||
5 | 11 | 1952 | WB | 1967? | RB | hand search |
6 | 17 | 1952 | WB | 1967? | RB | hand search |
7 | 25 | 1952 | WB | 1967? | RB | hand search |
8 | 34 | 1952 | WB | 1972 | WM | hand search |
9 | 44 | 1972 | WM | 1972 | WM | computer search |
10 | 55 | 1967 | RB | 1972 | WM | projective plane construction p=9 |
11 | 72 | 1967 | RB | 1972 | WM | projective plane construction p=11 |
12 | 85 | 1967 | RB | 1979 | JR1 | projective plane construction p=11 |
13 | 106 | 1981 | JR2 | 1981 | JR2 | computer search |
14 | 127 | 1967 | RB | 1985 | JS1 | projective plane construction p=13 |
15 | 151 | 1985 | JS1 | 1985 | JS1 | computer search |
16 | 177 | 1986 | JS1 | 1986 | JS1 | computer search |
17 | 199 | 1984? | AH | 1993 | OS | affine plane construction p=17 |
18 | 216 | 1967 | RB | 1993 | OS | projective plane construction p=17 |
19 | 246 | 1967 | RB | 1994 | DRM | projective plane construction p=19 |
20 | 283 | 1967 | RB | 1997? | GV | projective plane construction p=19 |
21 | 333 | 1967 | RB | 1998 | GV | projective plane construction p=23 |
22 | 356 | 1984? | AH | 1999 | GV | affine plane construction p=23 |
23 | 372 | 1967 | RB | 1999 | GV | projective plane construction p=23 |
24 | 425 | 1967 | RB | projective plane construction p=23 | ||
25 | 480 | 1984 | AH | projective plane construction p=25 | ||
26 | 492 | 1984 | AH | projective plane construction p=25 | ||
27 | 553 | 1984 | AH | projective plane construction p=27 | ||
28 | 585 | 1984 | AH | projective plane construction p=27 | ||
29 | 623 | 1984 | AH | projective plane construction p=29 | ||
30 | 680 | 1984 | AH | projective plane construction p=29 | ||
31 | 747 | 1984 | AH | projective plane construction p=31 | ||
32 | 784 | 1984 | AH | projective plane construction p=31 | ||
33 | 859 | 1984 | AH | projective plane construction p=32 | ||
34 | 938 | 1984 | AH | projective plane construction p=37 | ||
35 | 987 | 1984 | AH | affine plane construction p=37 | ||
36 | 1005 | 1984 | AH | affine plane construction p=37 | ||
37 | 1099 | 1984 | AH | projective plane construction p=37 | ||
38 | 1146 | 1984 | AH | projective plane construction p=37 | ||
39 | 1252 | 1984 | AH | projective plane construction p=41 | ||
40 | 1282 | 1984 | AH | affine plane construction p=41 | ||
41 | 1305 | 1984 | AH | projective plane construction p=41 | ||
42 | 1397 | 1984 | AH | projective plane construction p=41 | ||
43 | 1507 | 1984 | AH | affine plane construction p=43 | ||
44 | 1596 | 1984 | AH | projective plane construction p=43 | ||
45 | 1687 | 1984 | AH | projective plane construction p=47 | ||
46 | 1703 | 1984 | AH | projective plane construction p=47 | ||
47 | 1804 | 1984 | AH | affine plane construction p=47 | ||
48 | 1887 | 1986 | LS | projective plane construction p=49 | ||
49 | 1958 | 1984 | AH | projective plane construction p=49 | ||
50 | 2094 | 1984 | AH | projective plane construction p=49 | ||
51 | 2190 | 1984 | AH | projective plane construction p=53 | ||
52 | 2270 | 1984 | AH | projective plane construction p=53 | ||
53 | 2347 | 1984 | AH | projective plane construction p=53 | ||
54 | 2373 | 1984 | AH | projective plane construction p=53 | ||
55 | 2598 | 1984 | AH | projective plane construction p=59 | ||
56 | 2725 | 1984 | AH | projective plane construction p=59 | ||
57 | 2773 | 1984 | AH | projective plane construction p=59 | ||
58 | 2851 | 1984 | AH | projective plane construction p=59 | ||
59 | 2911 | 1984 | AH | projective plane construction p=59 | ||
60 | 3019 | 1984 | AH | projective plane construction p=59 | ||
61 | 3134 | 1984 | AH | affine plane construction p=61 | ||
62 | 3215 | 1984 | AH | projective plane construction p=61 | ||
63 | 3391 | 1984 | AH | projective plane construction p=64 | ||
64 | 3527 | 1984 | AH | projective plane construction p=64 | ||
65 | 3593 | 1984 | AH | projective plane construction p=64 | ||
66 | 3757 | 1984 | AH | projective plane construction p=67 | ||
67 | 3819 | 1984 | AH | projective plane construction p=67 | ||
68 | 3956 | 1984 | AH | projective plane construction p=67 | ||
69 | 4145 | 1984 | AH | projective plane construction p=71 | ||
70 | 4217 | 1984 | AH | projective plane construction p=71 | ||
71 | 4330 | 1984 | AH | projective plane construction p=71 | ||
72 | 4473 | 1986 | LS | projective plane construction p=73 | ||
73 | 4513 | 1984 | AH | projective plane construction p=73 | ||
74 | 4753 | 1984 | AH | projective plane construction p=73 | ||
75 | 4982 | 1984 | AH | projective plane construction p=79 | ||
76 | 5089 | 1984 | AH | projective plane construction p=79 | ||
77 | 5204 | 1984 | AH | projective plane construction p=79 | ||
78 | 5299 | 1984 | AH | projective plane construction p=79 | ||
79 | 5408 | 1984 | AH | projective plane construction p=79 | ||
80 | 5563 | 1984 | AH | projective plane construction p=79 | ||
81 | 5717 | 1984 | AH | projective plane construction p=83 | ||
82 | 5814 | 1984 | AH | projective plane construction p=83 | ||
83 | 6020 | 1984 | AH | projective plane construction p=83 | ||
84 | 6159 | 1984 | AH | projective plane construction p=83 | ||
85 | 6410 | 1984 | AH | affine plane construction p=89 | ||
86 | 6537 | 1984 | AH | affine plane construction p=89 | ||
87 | 6708 | 1984 | AH | projective plane construction p=89 | ||
88 | 6745 | 1984 | AH | projective plane construction p=89 | ||
89 | 6778 | 1984 | AH | projective plane construction p=89 | ||
90 | 6967 | 1984 | AH | projective plane construction p=89 | ||
91 | 7542 | 1984 | AH | affine plane construction p=97 | ||
92 | 7617 | 1984 | AH | projective plane construction p=97 | ||
93 | 7726 | 1984 | AH | projective plane construction p=97 | ||
94 | 7884 | 1984 | AH | projective plane construction p=97 | ||
95 | 7967 | 1984 | AH | projective plane construction p=97 | ||
96 | 8121 | 1984 | AH | affine plane construction p=97 | ||
97 | 8357 | 1984 | AH | projective plane construction p=97 | ||
98 | 8462 | 1986 | LS | projective plane construction p=101 | ||
99 | 8540 | 1984 | AH | projective plane construction p=101 | ||
100 | 8831 | 1984 | AH | projective plane construction p=101 | ||
101 | 8897 | 1986 | AH | projective plane construction p=101 | ||
102 | 9218 | 1986 | AH | projective plane construction p=101 | ||
103 | 9408 | 1986 | LS | projective plane construction p=103 | ||
104 | 9581 | 1986 | LS | projective plane construction p=103 | ||
105 | 9884 | 1997 | LM | affine plane construction p=107 | ||
106 | 10135 | 1986 | LS | projective plane construction p=107 | ||
107 | 10241 | 1997 | LM | projective plane construction p=109 | ||
108 | 10415 | 1986 | LS | projective plane construction p=109 | ||
109 | 10583 | 1986 | LS | projective plane construction p=109 | ||
110 | 10767 | 1997 | LM | projective plane construction p=109 | ||
111 | 11108 | 1986 | LS | projective plane construction p=113 | ||
112 | 11292 | 1986 | LS | projective plane construction p=113 | ||
113 | 11423 | 1986 | LS | projective plane construction p=113 | ||
114 | 11764 | 1986 | LS | projective plane construction p=113 | ||
115 | 12212 | 1986 | LS | projective plane construction p=121 | ||
116 | 12412 | 1986 | LS | projective plane construction p=121 | ||
117 | 12517 | 1986 | LS | projective plane construction p=121 | ||
118 | 12741 | 1998 | JS2 | projective plane construction p=125 | ||
119 | 12911 | 1986 | LS | projective plane construction p=121 | ||
120 | 13089 | 1986 | LS | projective plane construction p=121 | ||
121 | 13280 | 1986 | LS | projective plane construction p=121 | ||
122 | 13521 | 1986 | LS | projective plane construction p=125 | ||
123 | 13761 | 1997 | LM | affine plane construction p=127 | ||
124 | 13948 | 1998 | JS2 | affine plane construction p=125 | ||
125 | 14055 | 1986 | LS | projective plane construction p=125 | ||
126 | 14348 | 1986 | LS | projective plane construction p=127 | ||
127 | 14460 | 1998 | JS2 | projective plane construction p=128 | ||
128 | 14821 | 1986 | LS | projective plane construction p=128 | ||
129 | 15075 | 1986 | LS | projective plane construction p=128 | ||
130 | 15275 | 1986 | LS | projective plane construction p=131 | ||
131 | 15548 | 1986 | LS | projective plane construction p=131 | ||
132 | 15893 | 1986 | LS | projective plane construction p=131 | ||
133 | 16192 | 1986 | LS | projective plane construction p=137 | ||
134 | 16296 | 1986 | LS | projective plane construction p=137 | ||
135 | 16622 | 1997 | LM | projective plane construction p=139 | ||
136 | 16766 | 1986 | LS | projective plane construction p=137 | ||
137 | 17031 | 1997 | LM | projective plane construction p=139 | ||
138 | 17124 | 1986 | LS | projective plane construction p=139 | ||
139 | 17579 | 1997 | LM | affine plane construction p=139 | ||
140 | 17938 | 1986 | LS | projective plane construction p=139 | ||
141 | 18601 | 1986 | LS | projective plane construction p=149 | ||
142 | 18751 | 1986 | LS | projective plane construction p=149 | ||
143 | 18941 | 1997 | LM | affine plane construction p=149 | ||
144 | 19123 | 1997 | LM | projective plane construction p=151 | ||
145 | 19325 | 1986 | LS | projective plane construction p=149 | ||
146 | 19628 | 1986 | LS | projective plane construction p=149 | ||
147 | 19757 | 1986 | LS | projective plane construction p=149 | ||
148 | 20037 | 1986 | LS | projective plane construction p=149 | ||
149 | 20265 | 1997 | LM | projective plane construction p=151 | ||
150 | 20521 | 1986 | LS | projective plane construction p=149 |
References for above table.