MinT - Best Known (160−80, 160, s)-Nets in Base 8

Best Known (160−80, 160, s)-Nets in Base 8

(160−80, 160, 130)-Net over F₈ — Constructive and digital

Digital (80, 160, 130)-net over F₈, using

trace code for nets [i] based on digital (0, 80, 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]

(160−80, 160, 225)-Net in Base 8 — Constructive

(80, 160, 225)-net in base 8, using

base change [i] based on digital (40, 120, 225)-net over F₁₆, using
- net from sequence [i] based on digital (40, 224)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225, using
    - a function field by GarcÃa and Quoos [i]

(160−80, 160, 258)-Net over F₈ — Digital

Digital (80, 160, 258)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(160−80, 160, 9201)-Net in Base 8 — Upper bound on s

There is no (80, 160, 9202)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3 126520 344809 412162 471245 256400 550683 560779 125904 621343 287784 261924 540108 058462 441268 829263 967535 980087 203839 893804 166913 595761 143646 754976 932558 > 8¹⁶⁰ [i]