MinT - Best Known (239−57, 239, s)-Nets in Base 2

Best Known (239−57, 239, s)-Nets in Base 2

(239−57, 239, 195)-Net over F₂ — Constructive and digital

Digital (182, 239, 195)-net over F₂, using

13 times m-reduction [i] based on digital (182, 252, 195)-net over F₂, using
- trace code for nets [i] based on digital (14, 84, 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]

(239−57, 239, 368)-Net over F₂ — Digital

Digital (182, 239, 368)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(239−57, 239, 4049)-Net in Base 2 — Upper bound on s

There is no (182, 239, 4050)-net in base 2, because

1 times m-reduction [i] would yield (182, 238, 4050)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 444632 585843 645471 027732 779956 104072 022698 773702 144554 451152 146162 671888 > 2²³⁸ [i]