MinT - Best Known (136, 174, s)-Nets in Base 2

Best Known (136, 174, s)-Nets in Base 2

(136, 174, 196)-Net over F₂ — Constructive and digital

Digital (136, 174, 196)-net over F₂, using

2² times duplication [i] based on digital (134, 172, 196)-net over F₂, using
- trace code for nets [i] based on digital (5, 43, 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]

(136, 174, 358)-Net over F₂ — Digital

Digital (136, 174, 358)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(136, 174, 4501)-Net in Base 2 — Upper bound on s

There is no (136, 174, 4502)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 24023 051603 031743 677673 977972 972331 379044 907356 757474 > 2¹⁷⁴ [i]