Perfect and Optimal Rulers

Note that we use the number of segments S rather
than the number of marks M as our primary id.
The number of marks is M = S + 1.
* includes at least one ruler of Wichmann type.

Seg-
ment		 Length Perfect
Optimal		 Sum
0 0 1 1
1 1 1 1
2 2 1 3
3 2*
3 4 3 9
5 4
6 2*
4 7 12 24
8 8
9 4*
5 10 38 88
11 30
12 14*
13 6
6 14 130 254
15 80*
16 32
17 12
7 18 500* 1064
19 326
20 150
21 66
22 18*
23 4
8 24 944 1644
25 460
26 166
27 56
28 12
29 6*
9 30 2036 3382
31 890
32 304
33 120
34 20
35 10
36 2*
10 37 2678 4156
38 974
39 362
40 100
41 36
42 4
43 2*
       
       
       
       
Seg-
ment		 Length Perfect
Optimal		 Sum
11 44 4892 8022
45 2114
46 684*
47 238
48 68
49 22
50 4*
12 51 16318 26264
52 6350
53 2286
54 836
55 330
56 108
57 24*
58 12
13 59 31980 52012
60 12252
61 4960
62 1806
63 668
64 238*
65 86
66 6
67 12
68 4*
14 69 15558 25434
70 5906
71 2558*
72 850
73 388
74 120
75 38
76 4
77 6
78 4
79 2*
15 80 4972 8506
81 2234
82 798
83 332
84 106
85 48
86 4
87 6
88 2
89 2
90 2*
       
Seg-
ment		 Length Perfect
Optimal		 Sum
16 91 3392 5632
92 1262
93 626
94 212
95 76
96 40
97 16
98 2
99 2
100 2
101 2*
17 102 3426 6224
103 1506
104 682
105 360
106 138
107 70
108 28*
109 8
110 2
111 2
112 2*
18 113 6578 12330
114 2984
115 1458
116 586
117 374
118 192
119 98
120 38
121 14
122 4
123 4*
19 124 X X
125 X
126 X
127 X
128 X
129 X
130 X
131 X
132 X
133 X
134 X*
135 X
136 X
137 2
138 2*
Seg-
ment		 Length Perfect
Optimal		 Sum
20 139 X X
140 X
141 X
142 X
143 X
144 X
145 X*
146 X
147 X
148 X
149 X
150 X
151 X
152 X
153 X*
21 154 X X
155 X
156 X*
157 X
158 X
159 X
160 X
161 X
162 X
163 X
164 X
165 X
166 X
167 X
168 X*
22 169 X X
170 X
171 X
172 X
173 X
174 X
175 X*
176 X
177 X
178 X
179 X
180 X
181 X
182 X
183 X*
       
       
       

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