MinT - Best Known (26, 58, s)-Nets in Base 8

Best Known (26, 58, s)-Nets in Base 8

(26, 58, 65)-Net over F₈ — Constructive and digital

Digital (26, 58, 65)-net over F₈, using

t-expansion [i] based on digital (14, 58, 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]

(26, 58, 86)-Net over F₈ — Digital

Digital (26, 58, 86)-net over F₈, using

t-expansion [i] based on digital (25, 58, 86)-net over F₈, using
- net from sequence [i] based on digital (25, 85)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 25 and N(F) ≥ 86, using
    - a curve from the manYPoints database [i]

(26, 58, 1814)-Net in Base 8 — Upper bound on s

There is no (26, 58, 1815)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 24003 583366 105283 785187 315977 962515 092506 240430 368901 > 8⁵⁸ [i]