MinT - Best Known (74, 74+26, s)-Nets in Base 2

Best Known (74, 74+26, s)-Nets in Base 2

(74, 74+26, 102)-Net over F₂ — Constructive and digital

Digital (74, 100, 102)-net over F₂, using

2¹ times duplication [i] based on digital (73, 99, 102)-net over F₂, using
- trace code for nets [i] based on digital (7, 33, 34)-net over F₈, using
  - net from sequence [i] based on digital (7, 33)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 7 and N(F) ≥ 34, using
      - a function field by SÃ©mirat [i]

(74, 74+26, 146)-Net over F₂ — Digital

Digital (74, 100, 146)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(74, 74+26, 1153)-Net in Base 2 — Upper bound on s

There is no (74, 100, 1154)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 276235 454759 625884 547174 949472 > 2¹⁰⁰ [i]