MinT - Best Known (76−35, 76, s)-Nets in Base 8

Best Known (76−35, 76, s)-Nets in Base 8

(76−35, 76, 208)-Net over F₈ — Constructive and digital

Digital (41, 76, 208)-net over F₈, using

trace code for nets [i] based on digital (3, 38, 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]

(76−35, 76, 226)-Net over F₈ — Digital

Digital (41, 76, 226)-net over F₈, using

trace code for nets [i] based on digital (3, 38, 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]

(76−35, 76, 9876)-Net in Base 8 — Upper bound on s

There is no (41, 76, 9877)-net in base 8, because

1 times m-reduction [i] would yield (41, 75, 9877)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 53 952638 424869 031648 323965 046973 938430 380369 419352 272397 743808 417012 > 8⁷⁵ [i]