MinT - Best Known (91−45, 91, s)-Nets in Base 8

Best Known (91−45, 91, s)-Nets in Base 8

(91−45, 91, 130)-Net over F₈ — Constructive and digital

Digital (46, 91, 130)-net over F₈, using

1 times m-reduction [i] based on digital (46, 92, 130)-net over F₈, using
- trace code for nets [i] based on digital (0, 46, 65)-net over F₆₄, using
  - net from sequence [i] based on digital (0, 64)-sequence over F₆₄, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 0 and N(F) ≥ 65, using
      - the rational function field F₆₄(x) [i]
    - Niederreiter sequence [i]

(91−45, 91, 170)-Net over F₈ — Digital

Digital (46, 91, 170)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(91−45, 91, 6386)-Net in Base 8 — Upper bound on s

There is no (46, 91, 6387)-net in base 8, because

1 times m-reduction [i] would yield (46, 90, 6387)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1897 998667 608088 301929 715124 278666 533721 578489 985821 787591 148022 175665 225732 749384 > 8⁹⁰ [i]