MinT - Best Known (211, 211+∞, s)-Nets in Base 2

Best Known (211, 211+∞, s)-Nets in Base 2

Digital (211, m, 66)-net over F₂ for arbitrarily large m, using

Digital (211, m, 91)-net over F₂ for arbitrarily large m, using

net from sequence [i] based on digital (211, 90)-sequence over F₂, using
- t-expansion [i] based on digital (190, 90)-sequence over F₂, using
  - base reduction for sequences [i] based on digital (50, 90)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 50 and N(F) ≥ 91, using
      - a curve from the manYPoints database [i]

There is no (211, m, 223)-net in base 2 for arbitrarily large m, because

m-reduction [i] would yield (211, 1773, 223)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2¹⁷⁷³, 223, S₂, 8, 1562), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 1230 750843 207539 928922 435802 647717 377774 072468 794186 599823 318040 955208 925010 938163 669183 628773 744558 743507 578510 857577 035212 461689 560849 604729 983448 855410 909048 874370 185000 662392 607711 088538 463540 270289 025722 118549 222942 483983 769465 068896 318440 570701 539644 429382 273010 119520 038506 562494 668145 565755 774934 718884 199574 529274 023570 253716 734046 864760 305107 965556 573062 165926 350002 042756 089888 094651 661644 832526 825444 650780 557110 743776 503739 332333 358720 124543 516002 474240 199939 227046 830090 801005 774710 511854 521519 567400 909274 408195 668316 258304 / 1563 > 2¹⁷⁷³ [i]