MinT - Best Known (77−31, 77, s)-Nets in Base 2

Best Known (77−31, 77, s)-Nets in Base 2

(77−31, 77, 42)-Net over F₂ — Constructive and digital

Digital (46, 77, 42)-net over F₂, using

1 times m-reduction [i] based on digital (46, 78, 42)-net over F₂, using
- trace code for nets [i] based on digital (7, 39, 21)-net over F₄, using
  - net from sequence [i] based on digital (7, 20)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 7 and N(F) ≥ 21, using
      - an explicitly constructive algebraic function field [i]

(77−31, 77, 43)-Net over F₂ — Digital

Digital (46, 77, 43)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(77−31, 77, 194)-Net in Base 2 — Upper bound on s

There is no (46, 77, 195)-net in base 2, because

1 times m-reduction [i] would yield (46, 76, 195)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 79700 303896 592986 478368 > 2⁷⁶ [i]