MinT - Best Known (206−51, 206, s)-Nets in Base 2

Best Known (206−51, 206, s)-Nets in Base 2

(206−51, 206, 195)-Net over F₂ — Constructive and digital

Digital (155, 206, 195)-net over F₂, using

t-expansion [i] based on digital (154, 206, 195)-net over F₂, using
- 4 times m-reduction [i] based on digital (154, 210, 195)-net over F₂, using
  - trace code for nets [i] based on digital (14, 70, 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]

(206−51, 206, 295)-Net over F₂ — Digital

Digital (155, 206, 295)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(206−51, 206, 2955)-Net in Base 2 — Upper bound on s

There is no (155, 206, 2956)-net in base 2, because

1 times m-reduction [i] would yield (155, 205, 2956)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 51 436209 709157 239924 095394 900527 490632 171691 685952 340157 830520 > 2²⁰⁵ [i]