MinT - Best Known (12, 12+14, s)-Nets in Base 8

Best Known (12, 12+14, s)-Nets in Base 8

(12, 12+14, 48)-Net over F₈ — Constructive and digital

Digital (12, 26, 48)-net over F₈, using

t-expansion [i] based on digital (11, 26, 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]

(12, 12+14, 49)-Net in Base 8 — Constructive

(12, 26, 49)-net in base 8, using

2 times m-reduction [i] based on (12, 28, 49)-net in base 8, using
- base change [i] based on digital (5, 21, 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]

(12, 12+14, 53)-Net over F₈ — Digital

Digital (12, 26, 53)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(12, 12+14, 1087)-Net in Base 8 — Upper bound on s

There is no (12, 26, 1088)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 302552 251857 100792 804209 > 8²⁶ [i]