MinT - Best Known (139, 139+41, s)-Nets in Base 2

Best Known (139, 139+41, s)-Nets in Base 2

(139, 139+41, 195)-Net over F₂ — Constructive and digital

Digital (139, 180, 195)-net over F₂, using

t-expansion [i] based on digital (138, 180, 195)-net over F₂, using
- 6 times m-reduction [i] based on digital (138, 186, 195)-net over F₂, using
  - trace code for nets [i] based on digital (14, 62, 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]

(139, 139+41, 327)-Net over F₂ — Digital

Digital (139, 180, 327)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(139, 139+41, 4077)-Net in Base 2 — Upper bound on s

There is no (139, 180, 4078)-net in base 2, because

1 times m-reduction [i] would yield (139, 179, 4078)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 767756 456336 179684 078932 210471 972731 434830 270972 176386 > 2¹⁷⁹ [i]