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

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

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

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, 70+70, 230)-Net over F₈ — Digital

Digital (70, 140, 230)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(70, 70+70, 8116)-Net in Base 8 — Upper bound on s

There is no (70, 140, 8117)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2 717387 006260 778598 868669 798326 479119 860471 875455 412720 218745 616265 352565 923903 097408 060086 281067 625876 489275 916396 531774 745012 > 8¹⁴⁰ [i]