MinT - Best Known (237−57, 237, s)-Nets in Base 2

Best Known (237−57, 237, s)-Nets in Base 2

(237−57, 237, 195)-Net over F₂ — Constructive and digital

Digital (180, 237, 195)-net over F₂, using

12 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]

(237−57, 237, 358)-Net over F₂ — Digital

Digital (180, 237, 358)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(237−57, 237, 3851)-Net in Base 2 — Upper bound on s

There is no (180, 237, 3852)-net in base 2, because

1 times m-reduction [i] would yield (180, 236, 3852)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 110855 065781 456233 477489 892301 415892 395333 534238 271012 744228 333259 331520 > 2²³⁶ [i]