MinT - Best Known (33, 33+27, s)-Nets in Base 8

Best Known (33, 33+27, s)-Nets in Base 8

(33, 33+27, 208)-Net over F₈ — Constructive and digital

Digital (33, 60, 208)-net over F₈, using

trace code for nets [i] based on digital (3, 30, 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]

(33, 33+27, 226)-Net over F₈ — Digital

Digital (33, 60, 226)-net over F₈, using

trace code for nets [i] based on digital (3, 30, 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]

(33, 33+27, 10153)-Net in Base 8 — Upper bound on s

There is no (33, 60, 10154)-net in base 8, because

1 times m-reduction [i] would yield (33, 59, 10154)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 191709 322826 330511 122299 435261 518789 877277 166089 006040 > 8⁵⁹ [i]