MinT - Best Known (139−65, 139, s)-Nets in Base 8

Best Known (139−65, 139, s)-Nets in Base 8

(139−65, 139, 208)-Net over F₈ — Constructive and digital

Digital (74, 139, 208)-net over F₈, using

3 times m-reduction [i] based on digital (74, 142, 208)-net over F₈, using
- trace code for nets [i] based on digital (3, 71, 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]

(139−65, 139, 303)-Net over F₈ — Digital

Digital (74, 139, 303)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(139−65, 139, 14313)-Net in Base 8 — Upper bound on s

There is no (74, 139, 14314)-net in base 8, because

1 times m-reduction [i] would yield (74, 138, 14314)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 42343 157015 931820 765025 790139 141791 412279 884720 822019 999990 844039 766475 621082 908615 963739 029504 163870 474400 403417 269292 083303 > 8¹³⁸ [i]