Optimal Wichmann Rulers

Segments
(Marks-1)
Length
L
Optimal
Wichmann(r,s)
1 1
2 2 - 3
3 4 - 6 (0,1)
4 7 - 9 (0,2)
5 10 - 13
6 14 - 17
7 18 - 23
8 24 - 29 (1,2)
9 30 - 36 (1,3)
10 37 - 43 (1,4)
11 44 - 50 (1,5)
12 51 - 58
13 59 - 68 (2,3)
14 69 - 79 (2,4)
15 80 - 90 (2,5)
16 91 - 101 (2,6)
17 102 - 112 (2,7)
18 113 - 123 (2,8) and (3,4)
19 124 - 138 (3,5)
20 139 - 153 (3,6)
21 154 - 168 (3,7)
22 169 - 183 (3,8)
23 184 - 198 (3,9)
24 199 - 213 (3,10) and (4,6)
25 214 - 232 (4,7)
26 233 - 251 (4,8)
27 251 - 270 (4,9)
28 271 - 289 (4,10)
29 290 - 308 (4,11)
30 309 - 327 (4,12) and (5,8)
31 328 - 350 (5,9)
32 351 - 373 (5,10)
33 374 - 396 (5,11)
34 397 - 419 (5,12)
35 420 - 442 (5,13)
36 443 - 465 (5,14) and (6,10)
37 466 - 492 (6,11)
38 493 - 519 (6,12)
39 520 - 546 (6,13)
40 547 - 573 (6,14)
41 574 - 600 (6,15)
42 601 - 627 (6,16) and (7,12)
43 628 - 658 (7,13)
44 659 - 689 (7,14)
45 690 - 720 (7,15)
46 721 - 751 (7,16)
47 752 - 782 (7,17)
48 783 - 813 (7,18) and (8,14)
49 814 - 848 (8,15)
50 849 - 883 (8,16)
51 884 - 918 (8,17)
52 919 - 953 (8,18)
53 953 - 988 (8,19)
54 989 - 1023 (8,20) and (9,16)
172 . - 10017 (27,62)
547 . - 100022 (86,201)
1731 . - 1000086 (294,553)
5476 . - 10000065 (921,1790)
17320 . - 100000045 (2917,5650)
54787 . - 1000000058 (9353,17373)
173353 . - 10000000084 (30091,52987)

W(r,s) = [1^r,r+1,(2r+1)^r,(4r+3)^s,(2r+2)^(r+1),1^r]
S = 4r+s+2; L = 4r(r+s+2)+3(s+1);
B. Wichmann. A note on restricted difference bases.
J. London Math.Soc.38,1962,465-466