MinT - Best Known (155, ∞, s)-Nets in Base 3

Best Known (155, ∞, s)-Nets in Base 3

Digital (155, m, 81)-net over F₃ for arbitrarily large m, using

net from sequence [i] based on digital (155, 80)-sequence over F₃, using
- t-expansion [i] based on digital (144, 80)-sequence over F₃, using
  - base reduction for sequences [i] based on digital (32, 80)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 32 and N(F) ≥ 81, using
      - F₄ from the tower of function fields by Bezerra and GarcÃa over F₉ [i]

Digital (155, m, 163)-net over F₃ for arbitrarily large m, using

net from sequence [i] based on digital (155, 162)-sequence over F₃, using
- t-expansion [i] based on digital (151, 162)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 151 and N(F) ≥ 163, using
    - Drinfeld modules of rank 1 [i]

There is no (155, m, 325)-net in base 3 for arbitrarily large m, because

m-reduction [i] would yield (155, 1618, 325)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3¹⁶¹⁸, 325, S₃, 5, 1463), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 2 908256 885013 018827 956955 006976 272196 880493 715452 328824 294006 335352 545235 374698 297246 972412 255126 150106 239466 035990 409112 137247 735096 475891 830414 452143 642820 133276 008689 212143 811032 794794 165797 510823 240032 040735 454669 400662 537618 634728 775757 533194 707111 523719 505300 384576 390096 967575 890452 657303 818188 965988 366364 422435 884816 357032 935979 454337 933629 524640 542819 728580 390389 023262 562134 460176 297518 261866 745389 860490 276730 497046 671114 621044 843712 097745 488023 486662 916918 026131 851685 241748 182574 256760 256069 394352 324355 857078 579863 721558 173311 505044 485622 549955 915855 347806 504937 712859 346863 317389 857614 483409 220345 652852 823938 811229 239815 810939 489432 158230 220232 329064 230883 877844 430620 753888 909557 599313 880123 002368 013591 723533 160938 720780 127816 761641 345441 610085 127663 192167 / 244 > 3¹⁶¹⁸ [i]