MinT - Best Known (70, 139, s)-Nets in Base 8

Best Known (70, 139, s)-Nets in Base 8

(70, 139, 130)-Net over F₈ — Constructive and digital

Digital (70, 139, 130)-net over F₈, using

1 times m-reduction [i] based on digital (70, 140, 130)-net over F₈, using
- trace code for nets [i] based on digital (0, 70, 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]

(70, 139, 235)-Net over F₈ — Digital

Digital (70, 139, 235)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(70, 139, 8929)-Net in Base 8 — Upper bound on s

There is no (70, 139, 8930)-net in base 8, because

1 times m-reduction [i] would yield (70, 138, 8930)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 42399 928663 721775 996009 818981 800676 799865 659873 021639 371473 841405 461610 833180 259615 344174 348028 885559 017853 816162 898707 186096 > 8¹³⁸ [i]