MinT - Best Known (129, ∞, s)-Nets in Base 3

Best Known (129, ∞, s)-Nets in Base 3

Digital (129, m, 78)-net over F₃ for arbitrarily large m, using

net from sequence [i] based on digital (129, 77)-sequence over F₃, using
- t-expansion [i] based on digital (121, 77)-sequence over F₃, using
  - base reduction for sequences [i] based on digital (22, 77)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
      - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

Digital (129, m, 120)-net over F₃ for arbitrarily large m, using

There is no (129, m, 272)-net in base 3 for arbitrarily large m, because

m-reduction [i] would yield (129, 1625, 272)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3¹⁶²⁵, 272, S₃, 6, 1496), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 12447 828976 440326 735339 680976 740807 345493 532591 177182 116394 317393 602962 847690 850988 168063 692085 685834 777000 024247 134117 702471 245387 514863 748619 927489 290498 615991 631868 597231 110228 495486 050826 651153 825289 070605 087275 715028 695178 464583 538074 986676 509626 734558 112583 988518 328908 017314 773809 059528 658105 857776 533394 200403 225402 955016 794724 010991 801244 497451 619136 033071 347693 306966 231047 752878 523097 903485 645628 037628 914506 532313 681037 453834 988344 576323 951299 367219 939792 028831 116050 375989 623901 804984 897905 129019 508185 763009 381176 627200 380531 168749 467485 160113 646460 955636 541669 951073 821357 138331 858250 268993 409462 651135 557596 339369 088779 055996 254539 238155 509401 146288 687918 994136 044691 327327 167464 703183 273192 431025 293912 590706 021929 448774 030563 512897 101670 399719 950202 311039 447699 / 499 > 3¹⁶²⁵ [i]