MinT - Best Known (233, ∞, s)-Nets in Base 2

Best Known (233, ∞, s)-Nets in Base 2

Digital (233, m, 88)-net over F₂ for arbitrarily large m, using

net from sequence [i] based on digital (233, 87)-sequence over F₂, using
- base reduction for sequences [i] based on digital (73, 87)-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 (233, m, 129)-net over F₂ for arbitrarily large m, using

net from sequence [i] based on digital (233, 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 (233, m, 245)-net in base 2 for arbitrarily large m, because

m-reduction [i] would yield (233, 1949, 245)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2¹⁹⁴⁹, 245, S₂, 8, 1716), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 108 908756 018247 017738 846148 203336 770782 086811 400433 254891 428664 284262 450149 669687 178192 163957 571087 731048 845824 449832 008621 676764 388452 260409 225286 287159 093667 567713 843163 725898 164898 469318 344995 825226 484764 950027 385635 169684 923415 807750 920524 215546 373027 173675 855864 878727 942740 615561 271603 993444 280713 823669 135460 288438 896000 099455 973899 344934 883918 247743 905728 557468 736814 599350 662600 958018 297080 960558 396369 360578 290449 890993 563568 232647 753320 070966 789685 437500 126048 349423 663930 422427 919271 087992 554522 023279 356965 538756 888541 585818 166909 329229 585029 430329 563346 261419 879853 337903 890432 / 1717 > 2¹⁹⁴⁹ [i]