MinT - Best Known (64, 64+22, s)-Nets in Base 2

Best Known (64, 64+22, s)-Nets in Base 2

(64, 64+22, 84)-Net over F₂ — Constructive and digital

Digital (64, 86, 84)-net over F₂, using

t-expansion [i] based on digital (63, 86, 84)-net over F₂, using
- 1 times m-reduction [i] based on digital (63, 87, 84)-net over F₂, using
  - trace code for nets [i] based on digital (5, 29, 28)-net over F₈, using
    - net from sequence [i] based on digital (5, 27)-sequence over F₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 5 and N(F) ≥ 28, using
        a function field by SÃ©mirat [i]

(64, 64+22, 137)-Net over F₂ — Digital

Digital (64, 86, 137)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(64, 64+22, 1092)-Net in Base 2 — Upper bound on s

There is no (64, 86, 1093)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 78 099446 662108 013644 574976 > 2⁸⁶ [i]