MinT - Best Known (58, 76, s)-Nets in Base 2

Best Known (58, 76, s)-Nets in Base 2

(58, 76, 102)-Net over F₂ — Constructive and digital

Digital (58, 76, 102)-net over F₂, using

2¹ times duplication [i] based on digital (57, 75, 102)-net over F₂, using
- trace code for nets [i] based on digital (7, 25, 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]

(58, 76, 157)-Net over F₂ — Digital

Digital (58, 76, 157)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(58, 76, 1431)-Net in Base 2 — Upper bound on s

There is no (58, 76, 1432)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 75667 121376 021685 364954 > 2⁷⁶ [i]