MinT - Best Known (41, 70, s)-Nets in Base 8

Best Known (41, 70, s)-Nets in Base 8

(41, 70, 256)-Net over F₈ — Constructive and digital

Digital (41, 70, 256)-net over F₈, using

2 times m-reduction [i] based on digital (41, 72, 256)-net over F₈, using
- trace code for nets [i] based on digital (5, 36, 128)-net over F₆₄, using
  - net from sequence [i] based on digital (5, 127)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
      - a function field by SÃ©mirat [i]

(41, 70, 300)-Net in Base 8 — Constructive

(41, 70, 300)-net in base 8, using

trace code for nets [i] based on (6, 35, 150)-net in base 64, using
- base change [i] based on digital (1, 30, 150)-net over F₁₂₈, using
  - net from sequence [i] based on digital (1, 149)-sequence over F₁₂₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 1 and N(F) ≥ 150, using
      - a function field by SÃ©mirat [i]

(41, 70, 322)-Net over F₈ — Digital

Digital (41, 70, 322)-net over F₈, using

trace code for nets [i] based on digital (6, 35, 161)-net over F₆₄, using
- net from sequence [i] based on digital (6, 160)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 6 and N(F) ≥ 161, using
    - a curve from the manYPoints database [i]

(41, 70, 24386)-Net in Base 8 — Upper bound on s

There is no (41, 70, 24387)-net in base 8, because

1 times m-reduction [i] would yield (41, 69, 24387)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 205 731174 095451 368851 792822 729561 448567 706954 894128 718539 500464 > 8⁶⁹ [i]