MinT - Best Known (30−17, 30, s)-Nets in Base 8

Best Known (30−17, 30, s)-Nets in Base 8

(30−17, 30, 48)-Net over F₈ — Constructive and digital

Digital (13, 30, 48)-net over F₈, using

t-expansion [i] based on digital (11, 30, 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]

(30−17, 30, 49)-Net in Base 8 — Constructive

(13, 30, 49)-net in base 8, using

2 times m-reduction [i] based on (13, 32, 49)-net in base 8, using
- base change [i] based on digital (5, 24, 49)-net over F₁₆, using
  - net from sequence [i] based on digital (5, 48)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 5 and N(F) ≥ 49, using
      - a function field by SÃ©mirat [i]

(30−17, 30, 56)-Net over F₈ — Digital

Digital (13, 30, 56)-net over F₈, using

net from sequence [i] based on digital (13, 55)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 13 and N(F) ≥ 56, using
  - a curve from the manYPoints database [i]

(30−17, 30, 1005)-Net in Base 8 — Upper bound on s

There is no (13, 30, 1006)-net in base 8, because

1 times m-reduction [i] would yield (13, 29, 1006)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 155 604102 863692 026757 029475 > 8²⁹ [i]