MinT - Best Known (128, 128+35, s)-Nets in Base 2

Best Known (128, 128+35, s)-Nets in Base 2

(128, 128+35, 196)-Net over F₂ — Constructive and digital

Digital (128, 163, 196)-net over F₂, using

1 times m-reduction [i] based on digital (128, 164, 196)-net over F₂, using
- trace code for nets [i] based on digital (5, 41, 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]

(128, 128+35, 357)-Net over F₂ — Digital

Digital (128, 163, 357)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(128, 128+35, 5278)-Net in Base 2 — Upper bound on s

There is no (128, 163, 5279)-net in base 2, because

1 times m-reduction [i] would yield (128, 162, 5279)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 5 849475 336039 822801 073718 788882 710029 147019 049392 > 2¹⁶² [i]