MinT - Best Known (40, 40+33, s)-Nets in Base 8

Best Known (40, 40+33, s)-Nets in Base 8

(40, 40+33, 208)-Net over F₈ — Constructive and digital

Digital (40, 73, 208)-net over F₈, using

1 times m-reduction [i] based on digital (40, 74, 208)-net over F₈, using
- trace code for nets [i] based on digital (3, 37, 104)-net over F₆₄, using
  - net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
      - a function field by SÃ©mirat [i]

(40, 40+33, 226)-Net over F₈ — Digital

Digital (40, 73, 226)-net over F₈, using

1 times m-reduction [i] based on digital (40, 74, 226)-net over F₈, using
- trace code for nets [i] based on digital (3, 37, 113)-net over F₆₄, using
  - net from sequence [i] based on digital (3, 112)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 113, using
      - a curve from the manYPoints database [i]

(40, 40+33, 11245)-Net in Base 8 — Upper bound on s

There is no (40, 73, 11246)-net in base 8, because

1 times m-reduction [i] would yield (40, 72, 11246)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 105429 088897 351657 301291 195991 470918 445213 314080 847116 621126 055958 > 8⁷² [i]