MinT - Best Known (50−27, 50, s)-Nets in Base 8

Best Known (50−27, 50, s)-Nets in Base 8

(50−27, 50, 65)-Net over F₈ — Constructive and digital

Digital (23, 50, 65)-net over F₈, using

t-expansion [i] based on digital (14, 50, 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]

(50−27, 50, 77)-Net over F₈ — Digital

Digital (23, 50, 77)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(50−27, 50, 81)-Net in Base 8

(23, 50, 81)-net in base 8, using

2 times m-reduction [i] based on (23, 52, 81)-net in base 8, using
- base change [i] based on digital (10, 39, 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]

(50−27, 50, 2044)-Net in Base 8 — Upper bound on s

There is no (23, 50, 2045)-net in base 8, because

1 times m-reduction [i] would yield (23, 49, 2045)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 178 908621 513219 032315 269930 062471 348350 299272 > 8⁴⁹ [i]