MinT - Best Known (112, ∞, s)-Nets in Base 3

Best Known (112, ∞, s)-Nets in Base 3

Digital (112, m, 74)-net over F₃ for arbitrarily large m, using

net from sequence [i] based on digital (112, 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 (112, m, 104)-net over F₃ for arbitrarily large m, using

There is no (112, m, 238)-net in base 3 for arbitrarily large m, because

m-reduction [i] would yield (112, 1183, 238)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3¹¹⁸³, 238, S₃, 5, 1071), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 758 662358 192125 856321 490721 638882 907757 469041 304898 907140 466759 477590 444319 122322 515994 336259 575247 487817 319858 595329 140275 373379 365355 804966 249256 623388 626019 660797 594368 062567 043038 216964 532187 925621 737987 060677 445882 888660 725810 630904 751386 591035 415225 865725 910856 490797 722531 859020 856126 785480 044697 032233 999033 047886 826577 992905 830645 195381 088854 663073 440607 793632 400434 968379 115863 063825 584169 598536 673734 196052 658825 921635 534349 888253 051963 369223 192483 173019 752058 556792 201340 911876 861179 001619 631267 483544 189596 928831 861954 218103 193191 184697 792023 060069 914333 / 268 > 3¹¹⁸³ [i]