MinT - Best Known (232, ∞, s)-Nets in Base 2

Best Known (232, ∞, s)-Nets in Base 2

Digital (232, m, 87)-net over F₂ for arbitrarily large m, using

net from sequence [i] based on digital (232, 86)-sequence over F₂, using
- base reduction for sequences [i] based on digital (73, 86)-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 (232, m, 129)-net over F₂ for arbitrarily large m, using

net from sequence [i] based on digital (232, 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 (232, m, 244)-net in base 2 for arbitrarily large m, because

m-reduction [i] would yield (232, 1941, 244)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2¹⁹⁴¹, 244, S₂, 8, 1709), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 213509 089806 371435 759090 938952 000340 660106 986301 177085 607611 203974 882495 319167 516413 239553 638730 772412 812285 528971 756337 126999 742919 777078 868741 051651 441341 167106 648744 498175 186594 340983 272738 609559 052389 959376 516702 877936 823790 638433 968623 452786 797957 421015 808823 236975 502462 652775 123045 337885 087980 097910 400049 035560 785522 940269 883843 962315 971360 677744 582212 190231 460831 184988 193305 075614 092518 270843 791331 833659 841568 941441 261960 412909 275499 544848 863966 202139 293903 477276 784453 515282 732636 679625 921733 174612 585349 856364 018946 988712 834070 193265 987306 793417 371276 457148 733963 897871 007744 / 855 > 2¹⁹⁴¹ [i]