# Optimal Wichmann Rulers

 Segments(Marks-1) LengthL 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