MinT - Best Known (237, 237+∞, s)-Nets in Base 2

Best Known (237, 237+∞, s)-Nets in Base 2

Digital (237, m, 92)-net over F₂ for arbitrarily large m, using

net from sequence [i] based on digital (237, 91)-sequence over F₂, using
- base reduction for sequences [i] based on digital (73, 91)-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 (237, m, 129)-net over F₂ for arbitrarily large m, using

net from sequence [i] based on digital (237, 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 (237, m, 249)-net in base 2 for arbitrarily large m, because

m-reduction [i] would yield (237, 1981, 249)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2¹⁹⁸¹, 249, S₂, 8, 1744), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 460751 911708 265594 288994 036727 493838 192549 981154 368343 697540 343910 486643 594655 445166 475593 416200 483686 143934 173665 928206 507251 414042 638476 814300 455737 044964 230212 206195 329736 941240 675597 948178 118679 928564 250135 534325 635787 033083 186617 193265 512735 764989 441133 038279 890239 752770 786726 851865 051440 282870 445178 123724 717146 493331 503689 643928 243980 269559 421075 635188 514615 518088 184938 641023 894954 425254 109381 490105 221393 706778 056764 263309 678467 428393 480762 541520 938875 962920 439103 455867 710862 755657 165128 223642 960387 092894 624083 797162 297220 311521 068077 562883 459795 220093 911993 524913 408278 111869 119504 580608 / 1745 > 2¹⁹⁸¹ [i]