MinT - Best Known (21, 21+76, s)-Nets in Base 8

Best Known (21, 21+76, s)-Nets in Base 8

(21, 21+76, 65)-Net over F₈ — Constructive and digital

Digital (21, 97, 65)-net over F₈, using

t-expansion [i] based on digital (14, 97, 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]

(21, 21+76, 76)-Net over F₈ — Digital

Digital (21, 97, 76)-net over F₈, using

t-expansion [i] based on digital (20, 97, 76)-net over F₈, using
- net from sequence [i] based on digital (20, 75)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 20 and N(F) ≥ 76, using
    - a curve from the manYPoints database [i]

(21, 21+76, 409)-Net in Base 8 — Upper bound on s

There is no (21, 97, 410)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 4000 276121 363518 314816 381703 943616 425487 227804 391929 334056 632910 386221 312030 343909 493840 > 8⁹⁷ [i]