MinT - Best Known (215, ∞, s)-Nets in Base 2

Best Known (215, ∞, s)-Nets in Base 2

Digital (215, m, 70)-net over F₂ for arbitrarily large m, using

net from sequence [i] based on digital (215, 69)-sequence over F₂, using
- base reduction for sequences [i] based on digital (73, 69)-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 (215, m, 129)-net over F₂ for arbitrarily large m, using

There is no (215, m, 227)-net in base 2 for arbitrarily large m, because

m-reduction [i] would yield (215, 1805, 227)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2¹⁸⁰⁵, 227, S₂, 8, 1590), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 5 212871 512158 236001 974974 025999 879096 118677 443281 759239 900824 407512 740886 243077 227483 287643 084857 013942 820180 204849 194359 207185 328616 867790 562611 279186 001276 113721 721051 193649 459022 010088 465188 522185 266623 855008 846135 081978 393767 091602 707132 309204 399883 171821 538586 703366 582874 504044 220948 996469 543993 762318 099094 717529 407473 595582 243811 854934 100003 167967 948630 054856 782528 231749 493498 047224 242775 757213 778484 475192 359102 401528 925747 203084 473998 462767 575995 589798 139346 845786 110004 711525 341246 340158 479370 994245 709783 115779 213469 513321 620134 952960 / 1591 > 2¹⁸⁰⁵ [i]