MinT - Best Known (126−29, 126, s)-Nets in Base 2

Best Known (126−29, 126, s)-Nets in Base 2

(126−29, 126, 144)-Net over F₂ — Constructive and digital

Digital (97, 126, 144)-net over F₂, using

3 times m-reduction [i] based on digital (97, 129, 144)-net over F₂, using
- trace code for nets [i] based on digital (11, 43, 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]

(126−29, 126, 240)-Net over F₂ — Digital

Digital (97, 126, 240)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(126−29, 126, 2925)-Net in Base 2 — Upper bound on s

There is no (97, 126, 2926)-net in base 2, because

1 times m-reduction [i] would yield (97, 125, 2926)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 42 633329 056211 000499 669629 370997 383144 > 2¹²⁵ [i]