MinT - Best Known (259, ∞, s)-Nets in Base 2

Best Known (259, ∞, s)-Nets in Base 2

Digital (259, m, 104)-net over F₂ for arbitrarily large m, using

net from sequence [i] based on digital (259, 103)-sequence over F₂, using
- t-expansion [i] based on digital (249, 103)-sequence over F₂, using
  - base reduction for sequences [i] 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 (259, m, 129)-net over F₂ for arbitrarily large m, using

net from sequence [i] based on digital (259, 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 (259, m, 271)-net in base 2 for arbitrarily large m, because

m-reduction [i] would yield (259, 2157, 271)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2²¹⁵⁷, 271, S₂, 8, 1898), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 40439 676873 417901 862860 681840 141864 819453 069347 365944 373747 522964 928912 391385 100227 120707 157712 651990 237008 057544 091092 839242 358666 208754 724185 117884 712208 167430 577471 843283 525854 242117 403685 430019 526318 243699 701862 513319 674883 675715 166537 210139 635095 928179 745787 984659 940841 959588 121744 867680 066238 984980 834384 715615 590101 515567 286262 683390 950751 615600 056565 278167 161278 299588 744714 657056 597564 019037 458173 819319 125229 725117 067034 101009 938480 280857 488190 011652 496717 901775 557302 178360 546802 979303 893276 261257 082056 643281 274145 052844 335449 781279 429325 149730 284390 938165 417256 339172 238384 235883 151332 735209 756243 869947 788613 135033 217144 857375 067357 577216 / 1899 > 2²¹⁵⁷ [i]