MinT - Best Known (26, 26+57, s)-Nets in Base 8

Best Known (26, 26+57, s)-Nets in Base 8

(26, 26+57, 65)-Net over F₈ — Constructive and digital

Digital (26, 83, 65)-net over F₈, using

t-expansion [i] based on digital (14, 83, 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+57, 86)-Net over F₈ — Digital

Digital (26, 83, 86)-net over F₈, using

t-expansion [i] based on digital (25, 83, 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+57, 694)-Net in Base 8 — Upper bound on s

There is no (26, 83, 695)-net in base 8, because

1 times m-reduction [i] would yield (26, 82, 695)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 113 329471 834481 169181 262763 683984 322809 952513 338744 690306 848299 652397 926812 > 8⁸² [i]