MinT - Best Known (182, 182+51, s)-Nets in Base 2

Best Known (182, 182+51, s)-Nets in Base 2

(182, 182+51, 260)-Net over F₂ — Constructive and digital

Digital (182, 233, 260)-net over F₂, using

2¹ times duplication [i] based on digital (181, 232, 260)-net over F₂, using
- t-expansion [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]

(182, 182+51, 453)-Net over F₂ — Digital

Digital (182, 233, 453)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(182, 182+51, 6289)-Net in Base 2 — Upper bound on s

There is no (182, 233, 6290)-net in base 2, because

1 times m-reduction [i] would yield (182, 232, 6290)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 6904 480071 159219 592262 806833 868615 403375 181662 378888 722264 381006 821168 > 2²³² [i]