MinT - Best Known (102, 102+∞, s)-Nets in Base 3

Best Known (102, 102+∞, s)-Nets in Base 3

Digital (102, m, 69)-net over F₃ for arbitrarily large m, using

net from sequence [i] based on digital (102, 68)-sequence over F₃, using
- base reduction for sequences [i] based on digital (17, 68)-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 (102, m, 104)-net over F₃ for arbitrarily large m, using

There is no (102, m, 218)-net in base 3 for arbitrarily large m, because

m-reduction [i] would yield (102, 1083, 218)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3¹⁰⁸³, 218, S₃, 5, 981), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 3181 531104 689889 924832 218008 178295 833640 422565 435003 397044 633507 189951 572527 420788 186361 761694 930737 885983 408461 216396 533064 682985 126036 150711 722608 440326 961815 247654 725437 583413 791311 065677 004026 867150 708160 779002 660107 420750 152897 907691 182931 226784 706587 881911 584177 813488 368649 861953 450418 740061 679132 320134 035372 109933 095568 029153 266989 414143 226700 706865 462231 585184 971981 460555 234090 082647 996426 319210 827890 425688 368222 416215 451346 337226 425537 809241 075895 301095 768413 620819 066894 476461 660738 844359 284324 609937 061881 / 491 > 3¹⁰⁸³ [i]