MinT - Best Known (77−19, 77, s)-Nets in Base 2

Best Known (77−19, 77, s)-Nets in Base 2

(77−19, 77, 84)-Net over F₂ — Constructive and digital

Digital (58, 77, 84)-net over F₂, using

t-expansion [i] based on digital (57, 77, 84)-net over F₂, using
- 1 times m-reduction [i] based on digital (57, 78, 84)-net over F₂, using
  - trace code for nets [i] based on digital (5, 26, 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]

(77−19, 77, 140)-Net over F₂ — Digital

Digital (58, 77, 140)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(77−19, 77, 1431)-Net in Base 2 — Upper bound on s

There is no (58, 77, 1432)-net in base 2, because

1 times m-reduction [i] would yield (58, 76, 1432)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 75667 121376 021685 364954 > 2⁷⁶ [i]