MinT - Best Known (238−57, 238, s)-Nets in Base 2

Best Known (238−57, 238, s)-Nets in Base 2

(238−57, 238, 195)-Net over F₂ — Constructive and digital

Digital (181, 238, 195)-net over F₂, using

t-expansion [i] based on digital (180, 238, 195)-net over F₂, using
- 11 times m-reduction [i] based on digital (180, 249, 195)-net over F₂, using
  - trace code for nets [i] based on digital (14, 83, 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]

(238−57, 238, 363)-Net over F₂ — Digital

Digital (181, 238, 363)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(238−57, 238, 3949)-Net in Base 2 — Upper bound on s

There is no (181, 238, 3950)-net in base 2, because

1 times m-reduction [i] would yield (181, 237, 3950)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 222368 195597 892446 501445 544916 080800 168612 622733 281275 020201 107541 293734 > 2²³⁷ [i]