MinT - Best Known (99, ∞, s)-Nets in Base 3

Best Known (99, ∞, s)-Nets in Base 3

Digital (99, m, 66)-net over F₃ for arbitrarily large m, using

net from sequence [i] based on digital (99, 65)-sequence over F₃, using
- base reduction for sequences [i] based on digital (17, 65)-sequence over F₉, using
  - s-reduction 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 (99, m, 96)-net over F₃ for arbitrarily large m, using

There is no (99, m, 212)-net in base 3 for arbitrarily large m, because

m-reduction [i] would yield (99, 1053, 212)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3¹⁰⁵³, 212, S₃, 5, 954), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 31 596886 955855 250799 252638 541165 076052 838431 331889 837966 251890 245763 650784 874295 758945 837341 907033 829021 681337 710498 228331 883387 166012 707545 184407 099602 822402 994207 962378 790252 354124 186290 866518 344328 137720 620589 957065 596706 613524 191470 105611 574333 310647 961497 487605 690729 632082 074708 441167 975301 614327 457220 640733 191493 515941 870497 636830 711152 358801 203463 111742 564991 087068 024668 658072 188860 439604 454277 101238 307913 027684 122018 236740 974730 279100 543926 866646 932850 106193 318765 068046 120854 654970 967276 339459 / 955 > 3¹⁰⁵³ [i]