MinT - Best Known (149, 149+55, s)-Nets in Base 2

Best Known (149, 149+55, s)-Nets in Base 2

(149, 149+55, 144)-Net over F₂ — Constructive and digital

Digital (149, 204, 144)-net over F₂, using

3 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]

(149, 149+55, 234)-Net over F₂ — Digital

Digital (149, 204, 234)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(149, 149+55, 1963)-Net in Base 2 — Upper bound on s

There is no (149, 204, 1964)-net in base 2, because

1 times m-reduction [i] would yield (149, 203, 1964)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 12 946185 110233 110121 590542 215469 327579 818263 259407 808852 402790 > 2²⁰³ [i]