MinT - Best Known (133−28, 133, s)-Nets in Base 2

Best Known (133−28, 133, s)-Nets in Base 2

(133−28, 133, 196)-Net over F₂ — Constructive and digital

Digital (105, 133, 196)-net over F₂, using

2¹ 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]

(133−28, 133, 325)-Net over F₂ — Digital

Digital (105, 133, 325)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(133−28, 133, 4357)-Net in Base 2 — Upper bound on s

There is no (105, 133, 4358)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 10916 576523 392418 486400 742998 104413 741952 > 2¹³³ [i]