MinT - Best Known (125, 125+∞, s)-Nets in Base 2

Best Known (125, 125+∞, s)-Nets in Base 2

Digital (125, m, 57)-net over F₂ for arbitrarily large m, using

net from sequence [i] based on digital (125, 56)-sequence over F₂, using
- t-expansion [i] based on digital (110, 56)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₂ with g(F)Â =Â 69, N(F)Â =Â 48, 1 place with degree 2, and 8 places with degree 6 [i] based on function field F/F₂ with g(F) = 69 and N(F) ≥ 48, using an explicitly constructive algebraic function field [i]

Digital (125, m, 80)-net over F₂ for arbitrarily large m, using

net from sequence [i] based on digital (125, 79)-sequence over F₂, using
- t-expansion [i] based on digital (121, 79)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 121 and N(F) ≥ 80, using
    - Drinfeld modules of rank 1 [i]

There is no (125, m, 136)-net in base 2 for arbitrarily large m, because

m-reduction [i] would yield (125, 942, 136)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2⁹⁴², 136, S₂, 7, 817), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 17844 202901 733396 753576 749977 798806 721575 122419 912733 508669 262311 791287 885924 852482 542019 773953 876207 077584 685482 315676 605455 022946 538868 493489 966973 228735 509395 650085 369518 487312 236918 011572 842442 870349 388217 246472 812984 482534 561057 885187 284183 896996 144541 265449 726953 885184 185776 209920 / 409 > 2⁹⁴² [i]