MinT - Best Known (77, 77+27, s)-Nets in Base 2

Best Known (77, 77+27, s)-Nets in Base 2

(77, 77+27, 102)-Net over F₂ — Constructive and digital

Digital (77, 104, 102)-net over F₂, using

1 times m-reduction [i] based on digital (77, 105, 102)-net over F₂, using
- trace code for nets [i] based on digital (7, 35, 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]

(77, 77+27, 151)-Net over F₂ — Digital

Digital (77, 104, 151)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(77, 77+27, 1356)-Net in Base 2 — Upper bound on s

There is no (77, 104, 1357)-net in base 2, because

1 times m-reduction [i] would yield (77, 103, 1357)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 10 168968 178453 189323 337136 413450 > 2¹⁰³ [i]