MinT - Best Known (156, 156+72, s)-Nets in Base 2

Best Known (156, 156+72, s)-Nets in Base 2

(156, 156+72, 112)-Net over F₂ — Constructive and digital

Digital (156, 228, 112)-net over F₂, using

18 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]

(156, 156+72, 177)-Net over F₂ — Digital

Digital (156, 228, 177)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(156, 156+72, 1099)-Net in Base 2 — Upper bound on s

There is no (156, 228, 1100)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 443 664246 799093 129101 795179 441108 801101 969623 896781 938993 384668 835100 > 2²²⁸ [i]