MinT - Best Known (248, ∞, s)-Nets in Base 2

Best Known (248, ∞, s)-Nets in Base 2

Digital (248, m, 103)-net over F₂ for arbitrarily large m, using

net from sequence [i] based on digital (248, 102)-sequence over F₂, using
- base reduction for sequences [i] based on digital (73, 102)-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 (248, m, 129)-net over F₂ for arbitrarily large m, using

net from sequence [i] based on digital (248, 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 (248, m, 260)-net in base 2 for arbitrarily large m, because

m-reduction [i] would yield (248, 2069, 260)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2²⁰⁶⁹, 260, S₂, 8, 1821), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 68 315863 307793 717755 370475 518016 747630 499264 968415 160103 101819 919416 379058 377371 723429 899713 254725 824331 336027 176746 517581 156876 285262 898845 657559 425173 148161 741264 018450 738704 252559 598326 160972 632138 395400 043461 498385 845750 093765 329305 571883 868969 677559 009679 984758 322848 179680 545906 276594 169294 758969 246704 918117 601584 221593 378130 933542 207725 638832 239115 360292 395922 184429 999284 027660 428458 769853 410633 126845 614449 068782 758849 851714 094277 714922 205719 443043 314101 810768 516614 207352 661256 927530 444178 708099 961289 550230 230980 603929 427596 022532 012754 013892 817406 815795 972292 878495 868049 547679 268348 319341 876237 981189 147193 245696 / 911 > 2²⁰⁶⁹ [i]