MinT - Best Known (68−38, 68, s)-Nets in Base 8

Best Known (68−38, 68, s)-Nets in Base 8

(68−38, 68, 65)-Net over F₈ — Constructive and digital

Digital (30, 68, 65)-net over F₈, using

t-expansion [i] based on digital (14, 68, 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]

(68−38, 68, 97)-Net over F₈ — Digital

Digital (30, 68, 97)-net over F₈, using

t-expansion [i] based on digital (28, 68, 97)-net over F₈, using
- net from sequence [i] based on digital (28, 96)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 28 and N(F) ≥ 97, using
    - a curve from the manYPoints database [i]

(68−38, 68, 1921)-Net in Base 8 — Upper bound on s

There is no (30, 68, 1922)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 25 889726 714621 598624 364353 800522 304426 477268 303581 672755 072832 > 8⁶⁸ [i]