MinT - Best Known (173−70, 173, s)-Nets in Base 8

Best Known (173−70, 173, s)-Nets in Base 8

(173−70, 173, 354)-Net over F₈ — Constructive and digital

Digital (103, 173, 354)-net over F₈, using

8¹ times duplication [i] based on 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]

(173−70, 173, 384)-Net in Base 8 — Constructive

(103, 173, 384)-net in base 8, using

8¹ times duplication [i] based on (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]

(173−70, 173, 684)-Net over F₈ — Digital

Digital (103, 173, 684)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(173−70, 173, 57789)-Net in Base 8 — Upper bound on s

There is no (103, 173, 57790)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 717227 634440 467823 257337 073050 570810 801450 672990 552758 645359 285015 248782 970527 493164 220464 408158 942755 706170 160226 684188 993880 150714 333247 254031 446589 045990 > 8¹⁷³ [i]