MinT - Best Known (220, ∞, s)-Nets in Base 2

Best Known (220, ∞, s)-Nets in Base 2

Digital (220, m, 75)-net over F₂ for arbitrarily large m, using

net from sequence [i] based on digital (220, 74)-sequence over F₂, using
- base reduction for sequences [i] based on digital (73, 74)-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 (220, m, 129)-net over F₂ for arbitrarily large m, using

net from sequence [i] based on digital (220, 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 (220, m, 232)-net in base 2 for arbitrarily large m, because

m-reduction [i] would yield (220, 1845, 232)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2¹⁸⁴⁵, 232, S₂, 8, 1625), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 2 815529 115230 995402 800974 757543 658279 064456 013710 396289 186385 089948 125716 985757 390400 700805 753670 422349 148533 956187 209524 874289 624878 586979 183478 571856 881751 551261 738780 168627 888518 078936 818173 498580 381807 696539 847043 792602 603546 190699 298016 711192 162823 953144 990070 533409 944446 955875 616175 089007 292207 475814 213691 731410 479447 515298 849607 886726 438449 252593 289233 894045 875082 469536 345538 393685 798698 247912 891781 836184 959363 634613 851178 680091 468405 514232 582069 477407 666358 424237 625221 282777 389532 032377 667772 426357 747315 829251 106561 924704 395473 569800 764879 011840 / 813 > 2¹⁸⁴⁵ [i]