MinT - Best Known (232−76, 232, s)-Nets in Base 2

Best Known (232−76, 232, s)-Nets in Base 2

(232−76, 232, 112)-Net over F₂ — Constructive and digital

Digital (156, 232, 112)-net over F₂, using

14 times m-reduction [i] based on digital (156, 246, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 123, 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]

(232−76, 232, 165)-Net over F₂ — Digital

Digital (156, 232, 165)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(232−76, 232, 979)-Net in Base 2 — Upper bound on s

There is no (156, 232, 980)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 7100 026005 001475 816945 546286 466010 606162 801357 775337 901424 910073 680184 > 2²³² [i]