MinT - Best Known (126, 126+45, s)-Nets in Base 2

Best Known (126, 126+45, s)-Nets in Base 2

(126, 126+45, 144)-Net over F₂ — Constructive and digital

Digital (126, 171, 144)-net over F₂, using

t-expansion [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]

(126, 126+45, 216)-Net over F₂ — Digital

Digital (126, 171, 216)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(126, 126+45, 1886)-Net in Base 2 — Upper bound on s

There is no (126, 171, 1887)-net in base 2, because

1 times m-reduction [i] would yield (126, 170, 1887)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1507 071226 495940 886735 801223 853796 865613 013146 183157 > 2¹⁷⁰ [i]