MinT - Best Known (28, 28+22, s)-Nets in Base 8

Best Known (28, 28+22, s)-Nets in Base 8

(28, 28+22, 208)-Net over F₈ — Constructive and digital

Digital (28, 50, 208)-net over F₈, using

trace code for nets [i] based on digital (3, 25, 104)-net over F₆₄, using
- net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
    - a function field by SÃ©mirat [i]

(28, 28+22, 226)-Net over F₈ — Digital

Digital (28, 50, 226)-net over F₈, using

trace code for nets [i] based on digital (3, 25, 113)-net over F₆₄, using
- net from sequence [i] based on digital (3, 112)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 113, using
    - a curve from the manYPoints database [i]

(28, 28+22, 8923)-Net in Base 8 — Upper bound on s

There is no (28, 50, 8924)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1427 557524 165255 267470 204211 457605 233035 960689 > 8⁵⁰ [i]