MinT - Best Known (218−47, 218, s)-Nets in Base 2

Best Known (218−47, 218, s)-Nets in Base 2

(218−47, 218, 260)-Net over F₂ — Constructive and digital

Digital (171, 218, 260)-net over F₂, using

2 times m-reduction [i] based on digital (171, 220, 260)-net over F₂, using
- trace code for nets [i] based on digital (6, 55, 65)-net over F₁₆, using
  - net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
      - the Hermitian function field over F₁₆ [i]

(218−47, 218, 447)-Net over F₂ — Digital

Digital (171, 218, 447)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(218−47, 218, 6491)-Net in Base 2 — Upper bound on s

There is no (171, 218, 6492)-net in base 2, because

1 times m-reduction [i] would yield (171, 217, 6492)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 210991 378298 773431 411593 119609 804963 341258 184963 950347 733030 229930 > 2²¹⁷ [i]