MinT - Best Known (136, 136+69, s)-Nets in Base 2

Best Known (136, 136+69, s)-Nets in Base 2

(136, 136+69, 112)-Net over F₂ — Constructive and digital

Digital (136, 205, 112)-net over F₂, using

1 times m-reduction [i] based on digital (136, 206, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 103, 56)-net over F₄, using
  - net from sequence [i] based on digital (33, 55)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56, using
      - F₅ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(136, 136+69, 140)-Net over F₂ — Digital

Digital (136, 205, 140)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(136, 136+69, 817)-Net in Base 2 — Upper bound on s

There is no (136, 205, 818)-net in base 2, because

1 times m-reduction [i] would yield (136, 204, 818)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 26 657456 474466 908488 578970 615939 976419 594902 731661 251620 184880 > 2²⁰⁴ [i]