MinT - Best Known (70, 70+68, s)-Nets in Base 8

Best Known (70, 70+68, s)-Nets in Base 8

(70, 70+68, 160)-Net over F₈ — Constructive and digital

Digital (70, 138, 160)-net over F₈, using

trace code for nets [i] based on digital (1, 69, 80)-net over F₆₄, using
- net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
    - a function field by SÃ©mirat [i]

(70, 70+68, 241)-Net over F₈ — Digital

Digital (70, 138, 241)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(70, 70+68, 8929)-Net in Base 8 — Upper bound on s

There is no (70, 138, 8930)-net in base 8, because

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]