MinT - Best Known (116, 116+35, s)-Nets in Base 2

Best Known (116, 116+35, s)-Nets in Base 2

(116, 116+35, 195)-Net over F₂ — Constructive and digital

Digital (116, 151, 195)-net over F₂, using

2 times m-reduction [i] based on digital (116, 153, 195)-net over F₂, using
- trace code for nets [i] based on digital (14, 51, 65)-net over F₈, using
  - net from sequence [i] based on digital (14, 64)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
      - the Suzuki function field over F₈ [i]

(116, 116+35, 271)-Net over F₂ — Digital

Digital (116, 151, 271)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(116, 116+35, 3226)-Net in Base 2 — Upper bound on s

There is no (116, 151, 3227)-net in base 2, because

1 times m-reduction [i] would yield (116, 150, 3227)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1429 858979 591541 285245 508326 954486 211602 413044 > 2¹⁵⁰ [i]