MinT - Best Known (173−71, 173, s)-Nets in Base 8

Best Known (173−71, 173, s)-Nets in Base 8

(173−71, 173, 354)-Net over F₈ — Constructive and digital

Digital (102, 173, 354)-net over F₈, using

8¹ times duplication [i] based on digital (101, 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]

(173−71, 173, 640)-Net over F₈ — Digital

Digital (102, 173, 640)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(173−71, 173, 54454)-Net in Base 8 — Upper bound on s

There is no (102, 173, 54455)-net in base 8, because

1 times m-reduction [i] would yield (102, 172, 54455)-net in base 8, but
- 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]