MinT - Best Known (204−47, 204, s)-Nets in Base 2

Best Known (204−47, 204, s)-Nets in Base 2

(204−47, 204, 195)-Net over F₂ — Constructive and digital

Digital (157, 204, 195)-net over F₂, using

t-expansion [i] based on digital (156, 204, 195)-net over F₂, using
- 9 times m-reduction [i] based on digital (156, 213, 195)-net over F₂, using
  - trace code for nets [i] based on digital (14, 71, 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]

(204−47, 204, 353)-Net over F₂ — Digital

Digital (157, 204, 353)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(204−47, 204, 4245)-Net in Base 2 — Upper bound on s

There is no (157, 204, 4246)-net in base 2, because

1 times m-reduction [i] would yield (157, 203, 4246)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 12 895128 630650 319561 426107 514568 130689 087755 358803 159856 215148 > 2²⁰³ [i]