MinT - Best Known (228, ∞, s)-Nets in Base 2

Best Known (228, ∞, s)-Nets in Base 2

Digital (228, m, 83)-net over F₂ for arbitrarily large m, using

net from sequence [i] based on digital (228, 82)-sequence over F₂, using
- base reduction for sequences [i] based on digital (73, 82)-sequence over F₄, using
  - s-reduction based on digital (73, 103)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
      - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

Digital (228, m, 129)-net over F₂ for arbitrarily large m, using

net from sequence [i] based on digital (228, 128)-sequence over F₂, using
- t-expansion [i] based on digital (215, 128)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 215 and N(F) ≥ 129, using
    - Drinfeld modules of rank 1 [i]

There is no (228, m, 240)-net in base 2 for arbitrarily large m, because

m-reduction [i] would yield (228, 1909, 240)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2¹⁹⁰⁹, 240, S₂, 8, 1681), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 50 453420 877294 231371 655865 088438 890307 555375 024676 468269 613008 050623 369589 807267 996149 949560 670587 039841 879075 706114 321546 198100 041156 194614 393801 693519 644103 399589 500104 605069 746830 413307 557526 955073 708102 738134 228651 160596 750910 899552 761267 055765 201298 120594 930891 066894 461541 161067 502639 076359 676526 115412 154326 751012 992975 435317 359800 205461 919023 052885 149942 432083 107894 492228 392932 584030 703969 582587 989869 683443 091476 204088 559999 998849 100645 442933 725796 923041 293079 418607 496917 245081 873632 211859 066428 094184 206097 514498 174007 149638 124272 971258 126414 535196 188055 695110 701056 / 841 > 2¹⁹⁰⁹ [i]