MinT - Best Known (84, 84+35, s)-Nets in Base 2

Best Known (84, 84+35, s)-Nets in Base 2

(84, 84+35, 75)-Net over F₂ — Constructive and digital

Digital (84, 119, 75)-net over F₂, using

1 times m-reduction [i] based on digital (84, 120, 75)-net over F₂, using
- trace code for nets [i] based on digital (4, 40, 25)-net over F₈, using
  - net from sequence [i] based on digital (4, 24)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 4 and N(F) ≥ 25, using
      - a function field by SÃ©mirat [i]

(84, 84+35, 123)-Net over F₂ — Digital

Digital (84, 119, 123)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(84, 84+35, 857)-Net in Base 2 — Upper bound on s

There is no (84, 119, 858)-net in base 2, because

1 times m-reduction [i] would yield (84, 118, 858)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 336988 750568 930739 780066 611654 260225 > 2¹¹⁸ [i]