MinT - Best Known (108, 108+∞, s)-Nets in Base 3

Best Known (108, 108+∞, s)-Nets in Base 3

Digital (108, m, 74)-net over F₃ for arbitrarily large m, using

net from sequence [i] based on digital (108, 73)-sequence over F₃, using
- t-expansion [i] based on digital (107, 73)-sequence over F₃, using
  - base reduction for sequences [i] based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

Digital (108, m, 104)-net over F₃ for arbitrarily large m, using

There is no (108, m, 230)-net in base 3 for arbitrarily large m, because

m-reduction [i] would yield (108, 1143, 230)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3¹¹⁴³, 230, S₃, 5, 1035), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 64 414943 816803 618770 895002 208118 550400 149229 871321 395496 786809 320422 320996 933432 161622 619619 684496 447799 684619 300679 952879 942988 831603 438291 958535 017230 115043 483634 772092 719624 460087 753320 671502 832731 354932 812774 577219 626881 732525 985454 479183 722918 443349 612946 151822 262340 073512 939444 000464 329230 466605 478200 729433 909679 651494 330799 178115 553930 464357 261978 304191 723423 420709 211650 992272 384477 378218 857134 758007 394808 035093 792505 706431 640903 375419 389221 522618 589562 170587 119148 015101 544633 722708 158252 410232 653410 875745 175627 541557 747818 685209 748576 / 259 > 3¹¹⁴³ [i]