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*
� � � �
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� � � �
� � � �
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 17358 34224
125 8472
126 4180
127 2148
128 980
129 510
130 260
131 180
132 92
133 32
134 8*
135 0
136 0
137 2
138 2*
Seg-
ment		 Length Perfect
Optimal		 Sum
20 139 4902 10150
140 2418
141 1448
142 654
143 378
144 192
145 110*
146 28
147 10
148 6
149 0
150 0
151 0
152 2
153 2*
21 154 2682 5470
155 1326
156 794*
157 394
158 160
159 72
160 22
161 8
162 6
163 2
164 0
165 0
166 0
167 2
168 2*
22 169 2094 4072
170 988
171 516
172 246
173 144
174 46
175 22*
176 8
177 2
178 2
179 0
180 0
181 0
182 2
183 2*
� � � �
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Seg-
ment		 Length Perfect
Optimal		 Sum
23 184 2168 4072
185 896
186 462
187 230
188 128
189 80
190 68
191 26
192 4
193 4
194 2
195 0
196 0
197 2
198* 2
24 199 - �
200 -
201 -
202 -
203 -
204 -
205 -
206 -
207 -
208 22
209 0
210 0
211 0
212 4
213 4*
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