MinT - Best Known (214−58, 214, s)-Nets in Base 2

Best Known (214−58, 214, s)-Nets in Base 2

(214−58, 214, 144)-Net over F₂ — Constructive and digital

Digital (156, 214, 144)-net over F₂, using

t-expansion [i] based on digital (155, 214, 144)-net over F₂, using
- 2 times m-reduction [i] based on digital (155, 216, 144)-net over F₂, using
  - trace code for nets [i] based on digital (11, 72, 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]

(214−58, 214, 241)-Net over F₂ — Digital

Digital (156, 214, 241)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(214−58, 214, 1900)-Net in Base 2 — Upper bound on s

There is no (156, 214, 1901)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 26476 820682 191072 830329 856473 289511 379997 020838 250150 361992 195628 > 2²¹⁴ [i]