MinT - Best Known (170−44, 170, s)-Nets in Base 2

Best Known (170−44, 170, s)-Nets in Base 2

(170−44, 170, 144)-Net over F₂ — Constructive and digital

Digital (126, 170, 144)-net over F₂, using

t-expansion [i] based on digital (125, 170, 144)-net over F₂, using
- 1 times m-reduction [i] based on digital (125, 171, 144)-net over F₂, using
  - trace code for nets [i] based on digital (11, 57, 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]

(170−44, 170, 224)-Net over F₂ — Digital

Digital (126, 170, 224)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(170−44, 170, 1886)-Net in Base 2 — Upper bound on s

There is no (126, 170, 1887)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1507 071226 495940 886735 801223 853796 865613 013146 183157 > 2¹⁷⁰ [i]