MinT - Best Known (180, 180+51, s)-Nets in Base 2

Best Known (180, 180+51, s)-Nets in Base 2

(180, 180+51, 260)-Net over F₂ — Constructive and digital

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]

(180, 180+51, 439)-Net over F₂ — Digital

Digital (180, 231, 439)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(180, 180+51, 5948)-Net in Base 2 — Upper bound on s

There is no (180, 231, 5949)-net in base 2, because

1 times m-reduction [i] would yield (180, 230, 5949)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1728 156787 881858 787905 176339 268593 404542 010563 390195 540921 393720 649414 > 2²³⁰ [i]