MinT - Best Known (178−46, 178, s)-Nets in Base 2

Best Known (178−46, 178, s)-Nets in Base 2

(178−46, 178, 144)-Net over F₂ — Constructive and digital

Digital (132, 178, 144)-net over F₂, using

t-expansion [i] based on digital (131, 178, 144)-net over F₂, using
- 2 times m-reduction [i] based on digital (131, 180, 144)-net over F₂, using
  - trace code for nets [i] based on digital (11, 60, 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]

(178−46, 178, 234)-Net over F₂ — Digital

Digital (132, 178, 234)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(178−46, 178, 1980)-Net in Base 2 — Upper bound on s

There is no (132, 178, 1981)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 384189 318963 823002 480410 752368 395211 119010 871468 258984 > 2¹⁷⁸ [i]