MinT - Best Known (26, 26+70, s)-Nets in Base 8

Best Known (26, 26+70, s)-Nets in Base 8

(26, 26+70, 65)-Net over F₈ — Constructive and digital

Digital (26, 96, 65)-net over F₈, using

t-expansion [i] based on digital (14, 96, 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, 26+70, 86)-Net over F₈ — Digital

Digital (26, 96, 86)-net over F₈, using

t-expansion [i] based on digital (25, 96, 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, 26+70, 574)-Net in Base 8 — Upper bound on s

There is no (26, 96, 575)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 521 282967 411880 797677 698429 712745 598629 192404 628278 124319 062428 081606 805562 635784 685092 > 8⁹⁶ [i]