MinT - Best Known (177−47, 177, s)-Nets in Base 2

Best Known (177−47, 177, s)-Nets in Base 2

(177−47, 177, 144)-Net over F₂ — Constructive and digital

Digital (130, 177, 144)-net over F₂, using

t-expansion [i] based on digital (129, 177, 144)-net over F₂, using
- trace code for nets [i] based on digital (11, 59, 48)-net over F₈, using
  - net from sequence [i] based on digital (11, 47)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 11 and N(F) ≥ 48, using
      - a function field by SÃ©mirat [i]

(177−47, 177, 217)-Net over F₂ — Digital

Digital (130, 177, 217)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(177−47, 177, 1862)-Net in Base 2 — Upper bound on s

There is no (130, 177, 1863)-net in base 2, because

1 times m-reduction [i] would yield (130, 176, 1863)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 95852 525629 565723 579931 606724 153454 857053 613307 997832 > 2¹⁷⁶ [i]