MinT - Best Known (172−70, 172, s)-Nets in Base 8

Best Known (172−70, 172, s)-Nets in Base 8

(172−70, 172, 354)-Net over F₈ — Constructive and digital

Digital (102, 172, 354)-net over F₈, using

t-expansion [i] based on digital (93, 172, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 86, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

(172−70, 172, 384)-Net in Base 8 — Constructive

(102, 172, 384)-net in base 8, using

trace code for nets [i] based on (16, 86, 192)-net in base 64, using
- 5 times m-reduction [i] based on (16, 91, 192)-net in base 64, using
  - base change [i] based on digital (3, 78, 192)-net over F₁₂₈, using
    - net from sequence [i] based on digital (3, 191)-sequence over F₁₂₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 3 and N(F) ≥ 192, using
        a function field by SÃ©mirat [i]

(172−70, 172, 662)-Net over F₈ — Digital

Digital (102, 172, 662)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(172−70, 172, 54454)-Net in Base 8 — Upper bound on s

There is no (102, 172, 54455)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 214614 672943 643722 203100 281542 205727 240357 287615 221027 533830 775298 246046 659598 531838 788209 095042 805692 838922 038298 620143 085464 374577 678399 592724 351143 034476 > 8¹⁷² [i]