MinT - Best Known (189, ∞, s)-Nets in Base 2

Best Known (189, ∞, s)-Nets in Base 2

Digital (189, m, 66)-net over F₂ for arbitrarily large m, using

Digital (189, m, 90)-net over F₂ for arbitrarily large m, using

net from sequence [i] based on digital (189, 89)-sequence over F₂, using
- base reduction for sequences [i] based on digital (50, 89)-sequence over F₄, using
  - s-reduction 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 (189, m, 200)-net in base 2 for arbitrarily large m, because

m-reduction [i] would yield (189, 1790, 200)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2¹⁷⁹⁰, 200, S₂, 9, 1601), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 57 493592 995337 589540 011470 827121 405018 612914 681206 012038 893841 014534 110223 392628 926678 426881 782427 061501 002107 436809 019818 044571 602540 923796 852402 189144 536758 124457 886628 048105 798475 517311 702732 852877 696496 482009 743343 253556 589013 932621 345881 716871 101027 821068 315946 927978 305329 323918 366843 415523 385176 543521 729239 042104 510367 447164 018878 180061 452800 153840 579265 998733 102942 523107 463667 898516 418018 326932 050085 336230 146178 916259 696233 586650 735617 297262 661855 142073 605477 864151 732379 609451 042134 927991 726546 695889 454373 642798 599763 555386 392576 / 801 > 2¹⁷⁹⁰ [i]