MinT - Best Known (69−34, 69, s)-Nets in Base 8

Best Known (69−34, 69, s)-Nets in Base 8

(69−34, 69, 130)-Net over F₈ — Constructive and digital

Digital (35, 69, 130)-net over F₈, using

1 times m-reduction [i] based on digital (35, 70, 130)-net over F₈, using
- trace code for nets [i] based on digital (0, 35, 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]

(69−34, 69, 138)-Net over F₈ — Digital

Digital (35, 69, 138)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(69−34, 69, 4735)-Net in Base 8 — Upper bound on s

There is no (35, 69, 4736)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 205 980026 098784 274017 121711 410971 526833 508368 690830 007424 567049 > 8⁶⁹ [i]