MinT - Best Known (181, 181+49, s)-Nets in Base 2

Best Known (181, 181+49, s)-Nets in Base 2

(181, 181+49, 260)-Net over F₂ — Constructive and digital

Digital (181, 230, 260)-net over F₂, using

t-expansion [i] based on digital (180, 230, 260)-net over F₂, using
- 2 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]

(181, 181+49, 483)-Net over F₂ — Digital

Digital (181, 230, 483)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(181, 181+49, 7270)-Net in Base 2 — Upper bound on s

There is no (181, 230, 7271)-net in base 2, because

1 times m-reduction [i] would yield (181, 229, 7271)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 863 391017 143680 040572 878180 948559 507353 287542 301729 519021 856119 263436 > 2²²⁹ [i]