MinT - Best Known (119, ∞, s)-Nets in Base 3

Best Known (119, ∞, s)-Nets in Base 3

Digital (119, m, 76)-net over F₃ for arbitrarily large m, using

net from sequence [i] based on digital (119, 75)-sequence over F₃, using
- base reduction for sequences [i] based on digital (22, 75)-sequence over F₉, using
  - s-reduction based on digital (22, 77)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
      - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

Digital (119, m, 120)-net over F₃ for arbitrarily large m, using

There is no (119, m, 252)-net in base 3 for arbitrarily large m, because

m-reduction [i] would yield (119, 1505, 252)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3¹⁵⁰⁵, 252, S₃, 6, 1386), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 21 131334 265537 412388 338894 228872 212597 545767 657054 632729 559160 685665 175078 463961 256344 494797 162346 900308 818615 469668 229909 150145 380023 637253 284318 805293 028707 279767 778376 840948 929763 443326 956667 323462 956122 800097 270470 246689 271580 690779 825683 756458 812987 339776 134210 294521 038590 168224 487763 359241 054308 197359 779762 200125 102091 018894 187519 085539 289920 651778 975468 008015 937272 156484 492804 298616 547862 921167 727747 761632 997045 267625 944204 115970 197598 718097 901968 507767 475364 395894 316809 064261 157620 931406 041134 830601 673930 792826 777227 360240 252908 899931 551575 100452 820852 491647 196077 355197 840192 595444 403668 917313 346485 478349 843310 917050 076442 335837 789904 525609 895771 749982 916929 150506 067172 552268 238502 908784 334953 280441 649587 / 1387 > 3¹⁵⁰⁵ [i]