MinT - Best Known (175−39, 175, s)-Nets in Base 2

Best Known (175−39, 175, s)-Nets in Base 2

(175−39, 175, 195)-Net over F₂ — Constructive and digital

Digital (136, 175, 195)-net over F₂, using

8 times m-reduction [i] based on digital (136, 183, 195)-net over F₂, using
- trace code for nets [i] based on digital (14, 61, 65)-net over F₈, using
  - net from sequence [i] based on digital (14, 64)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
      - the Suzuki function field over F₈ [i]

(175−39, 175, 340)-Net over F₂ — Digital

Digital (136, 175, 340)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(175−39, 175, 4501)-Net in Base 2 — Upper bound on s

There is no (136, 175, 4502)-net in base 2, because

1 times m-reduction [i] would yield (136, 174, 4502)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 24023 051603 031743 677673 977972 972331 379044 907356 757474 > 2¹⁷⁴ [i]