MinT - Best Known (150, 205, s)-Nets in Base 2

Best Known (150, 205, s)-Nets in Base 2

(150, 205, 144)-Net over F₂ — Constructive and digital

Digital (150, 205, 144)-net over F₂, using

t-expansion [i] based on digital (149, 205, 144)-net over F₂, using
- 2 times m-reduction [i] based on digital (149, 207, 144)-net over F₂, using
  - trace code for nets [i] based on digital (11, 69, 48)-net over F₈, using
    - net from sequence [i] based on digital (11, 47)-sequence over F₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 11 and N(F) ≥ 48, using
        a function field by SÃ©mirat [i]

(150, 205, 238)-Net over F₂ — Digital

Digital (150, 205, 238)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(150, 205, 2015)-Net in Base 2 — Upper bound on s

There is no (150, 205, 2016)-net in base 2, because

1 times m-reduction [i] would yield (150, 204, 2016)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 25 860232 912080 788276 377110 682926 284292 536124 635021 925958 789483 > 2²⁰⁴ [i]