MinT - Best Known (47−25, 47, s)-Nets in Base 8

Best Known (47−25, 47, s)-Nets in Base 8

(47−25, 47, 65)-Net over F₈ — Constructive and digital

Digital (22, 47, 65)-net over F₈, using

t-expansion [i] based on digital (14, 47, 65)-net over F₈, using
- net from sequence [i] based on digital (14, 64)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
    - the Suzuki function field over F₈ [i]

(47−25, 47, 78)-Net over F₈ — Digital

Digital (22, 47, 78)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(47−25, 47, 81)-Net in Base 8

(22, 47, 81)-net in base 8, using

1 times m-reduction [i] based on (22, 48, 81)-net in base 8, using
- base change [i] based on digital (10, 36, 81)-net over F₁₆, using
  - net from sequence [i] based on digital (10, 80)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 10 and N(F) ≥ 81, using
      - a curve from the manYPoints database [i]

(47−25, 47, 2181)-Net in Base 8 — Upper bound on s

There is no (22, 47, 2182)-net in base 8, because

1 times m-reduction [i] would yield (22, 46, 2182)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 350171 360984 304480 836752 250201 527715 176656 > 8⁴⁶ [i]