MinT - Best Known (139−29, 139, s)-Nets in Base 2

Best Known (139−29, 139, s)-Nets in Base 2

(139−29, 139, 196)-Net over F₂ — Constructive and digital

Digital (110, 139, 196)-net over F₂, using

1 times m-reduction [i] based on digital (110, 140, 196)-net over F₂, using
- trace code for nets [i] based on digital (5, 35, 49)-net over F₁₆, using
  - net from sequence [i] based on digital (5, 48)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 5 and N(F) ≥ 49, using
      - a function field by SÃ©mirat [i]

(139−29, 139, 345)-Net over F₂ — Digital

Digital (110, 139, 345)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(139−29, 139, 5586)-Net in Base 2 — Upper bound on s

There is no (110, 139, 5587)-net in base 2, because

1 times m-reduction [i] would yield (110, 138, 5587)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 348598 016002 319842 167227 254908 590915 978164 > 2¹³⁸ [i]