MinT - Best Known (129−27, 129, s)-Nets in Base 2

Best Known (129−27, 129, s)-Nets in Base 2

(129−27, 129, 196)-Net over F₂ — Constructive and digital

Digital (102, 129, 196)-net over F₂, using

2¹ times duplication [i] based on digital (101, 128, 196)-net over F₂, using
- trace code for nets [i] based on digital (5, 32, 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]

(129−27, 129, 324)-Net over F₂ — Digital

Digital (102, 129, 324)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(129−27, 129, 5197)-Net in Base 2 — Upper bound on s

There is no (102, 129, 5198)-net in base 2, because

1 times m-reduction [i] would yield (102, 128, 5198)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 340 531127 613588 462063 533895 254914 991403 > 2¹²⁸ [i]