MinT - Best Known (30, 30+24, s)-Nets in Base 8

Best Known (30, 30+24, s)-Nets in Base 8

(30, 30+24, 208)-Net over F₈ — Constructive and digital

Digital (30, 54, 208)-net over F₈, using

trace code for nets [i] based on digital (3, 27, 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]

(30, 30+24, 226)-Net over F₈ — Digital

Digital (30, 54, 226)-net over F₈, using

trace code for nets [i] based on digital (3, 27, 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]

(30, 30+24, 8746)-Net in Base 8 — Upper bound on s

There is no (30, 54, 8747)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 5 853888 624475 152259 434418 341163 429719 191236 782616 > 8⁵⁴ [i]