MinT - Best Known (134−28, 134, s)-Nets in Base 2

Best Known (134−28, 134, s)-Nets in Base 2

(134−28, 134, 196)-Net over F₂ — Constructive and digital

Digital (106, 134, 196)-net over F₂, using

2² times duplication [i] based on digital (104, 132, 196)-net over F₂, using
- trace code for nets [i] based on digital (5, 33, 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]

(134−28, 134, 334)-Net over F₂ — Digital

Digital (106, 134, 334)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(134−28, 134, 4579)-Net in Base 2 — Upper bound on s

There is no (106, 134, 4580)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 21817 634142 330863 938697 785883 834016 362904 > 2¹³⁴ [i]