MinT - Best Known (240−59, 240, s)-Nets in Base 2

Best Known (240−59, 240, s)-Nets in Base 2

(240−59, 240, 195)-Net over F₂ — Constructive and digital

Digital (181, 240, 195)-net over F₂, using

t-expansion [i] based on digital (180, 240, 195)-net over F₂, using
- 9 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]

(240−59, 240, 341)-Net over F₂ — Digital

Digital (181, 240, 341)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(240−59, 240, 3489)-Net in Base 2 — Upper bound on s

There is no (181, 240, 3490)-net in base 2, because

1 times m-reduction [i] would yield (181, 239, 3490)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 888746 974235 962324 592050 458229 983256 134601 247319 614789 273872 260789 886376 > 2²³⁹ [i]