MinT - Best Known (162, ∞, s)-Nets in Base 2

Best Known (162, ∞, s)-Nets in Base 2

Digital (162, m, 65)-net over F₂ for arbitrarily large m, using

net from sequence [i] based on digital (162, 64)-sequence over F₂, using
- base reduction for sequences [i] based on digital (49, 64)-sequence over F₄, using
  - s-reduction based on digital (49, 65)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 49 and N(F) ≥ 66, using
      - T₆ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

Digital (162, m, 81)-net over F₂ for arbitrarily large m, using

net from sequence [i] based on digital (162, 80)-sequence over F₂, using
- t-expansion [i] based on digital (126, 80)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 126 and N(F) ≥ 81, using
    - Drinfeld modules of rank 1 [i]

There is no (162, m, 173)-net in base 2 for arbitrarily large m, because

m-reduction [i] would yield (162, 1374, 173)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2¹³⁷⁴, 173, S₂, 8, 1212), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 559 079710 795581 503490 255379 757320 029736 346859 173601 528398 814855 719239 979837 164473 905762 005111 213593 630359 516346 709356 345010 590546 216949 691924 743511 170891 373193 218948 374815 142083 802024 600993 356446 081305 846322 657706 636476 351979 960358 267757 601865 188568 913506 859188 026023 590523 634277 408422 609221 590257 364376 418948 215047 281989 644755 002201 346627 269632 041711 130350 285331 720006 815202 410337 439700 132075 641152 966409 282968 879104 / 1213 > 2¹³⁷⁴ [i]