MinT - Best Known (238−58, 238, s)-Nets in Base 2

Best Known (238−58, 238, s)-Nets in Base 2

(238−58, 238, 195)-Net over F₂ — Constructive and digital

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]

(238−58, 238, 346)-Net over F₂ — Digital

Digital (180, 238, 346)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(238−58, 238, 3405)-Net in Base 2 — Upper bound on s

There is no (180, 238, 3406)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 442255 866941 320067 316108 780864 010925 145504 754551 993071 201467 568947 889228 > 2²³⁸ [i]