Best Known (40, 40+∞, s)-Nets in Base 8
(40, 40+∞, 98)-Net over F8 — Constructive and digital
Digital (40, m, 98)-net over F8 for arbitrarily large m, using
- net from sequence [i] based on digital (40, 97)-sequence over F8, using
- t-expansion [i] based on digital (37, 97)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 37 and N(F) ≥ 98, using
- t-expansion [i] based on digital (37, 97)-sequence over F8, using
(40, 40+∞, 129)-Net over F8 — Digital
Digital (40, m, 129)-net over F8 for arbitrarily large m, using
- net from sequence [i] based on digital (40, 128)-sequence over F8, using
- t-expansion [i] based on digital (38, 128)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 38 and N(F) ≥ 129, using
- t-expansion [i] based on digital (38, 128)-sequence over F8, using
(40, 40+∞, 303)-Net in Base 8 — Upper bound on s
There is no (40, m, 304)-net in base 8 for arbitrarily large m, because
- m-reduction [i] would yield (40, 908, 304)-net in base 8, but
- extracting embedded OOA [i] would yield OOA(8908, 304, S8, 3, 868), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1 296934 843950 346264 662297 107728 714610 647136 292511 915539 172662 706864 777333 749745 149937 911187 442033 458783 115726 561734 703889 310473 590130 187487 416855 546024 730362 426772 865767 960557 627114 297367 399828 257918 119474 120532 915791 751262 390003 488538 798077 694959 134542 970004 052464 143043 831235 005603 559775 768027 500691 302672 081145 659258 071158 847870 734401 745699 776519 331306 998132 576879 351194 889355 336327 248026 341391 389437 298809 922229 607159 790431 465274 495527 022387 112740 259432 261702 881711 072097 280617 476878 312950 619911 403193 696855 958336 480345 872460 863526 586072 717580 192944 277737 537414 690954 465293 556850 172953 096690 059454 386170 088292 848024 351675 216613 903991 256371 193086 171782 826740 249096 487705 628613 524613 708939 419273 703778 778440 998953 506283 502091 664153 007222 746491 588466 255350 706507 960819 727301 813575 702008 410544 187243 984682 703506 550867 099648 / 79 > 8908 [i]
- extracting embedded OOA [i] would yield OOA(8908, 304, S8, 3, 868), but