MinT - Best Known (231−49, 231, s)-Nets in Base 2

Best Known (231−49, 231, s)-Nets in Base 2

(231−49, 231, 260)-Net over F₂ — Constructive and digital

Digital (182, 231, 260)-net over F₂, using

t-expansion [i] based on digital (180, 231, 260)-net over F₂, using
- 1 times m-reduction [i] based on digital (180, 232, 260)-net over F₂, using
  - trace code for nets [i] based on digital (6, 58, 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]

(231−49, 231, 491)-Net over F₂ — Digital

Digital (182, 231, 491)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(231−49, 231, 7484)-Net in Base 2 — Upper bound on s

There is no (182, 231, 7485)-net in base 2, because

1 times m-reduction [i] would yield (182, 230, 7485)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1726 273704 774008 887035 417531 690181 101736 999533 338631 628515 192184 516313 > 2²³⁰ [i]