MinT - Best Known (168−66, 168, s)-Nets in Base 8

Best Known (168−66, 168, s)-Nets in Base 8

(168−66, 168, 354)-Net over F₈ — Constructive and digital

Digital (102, 168, 354)-net over F₈, using

t-expansion [i] based on digital (93, 168, 354)-net over F₈, using
- 4 times m-reduction [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]

(168−66, 168, 432)-Net in Base 8 — Constructive

(102, 168, 432)-net in base 8, using

t-expansion [i] based on (101, 168, 432)-net in base 8, using
- trace code for nets [i] based on (17, 84, 216)-net in base 64, using
  - base change [i] based on digital (5, 72, 216)-net over F₁₂₈, using
    - net from sequence [i] based on digital (5, 215)-sequence over F₁₂₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 5 and N(F) ≥ 216, using
        a function field by SÃ©mirat [i]

(168−66, 168, 767)-Net over F₈ — Digital

Digital (102, 168, 767)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(168−66, 168, 74419)-Net in Base 8 — Upper bound on s

There is no (102, 168, 74420)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 52 395843 851628 731959 190820 740103 412272 752385 010517 471863 556520 814298 793457 096971 653285 954113 413783 814846 388327 964909 473716 117533 008408 404421 309856 134455 > 8¹⁶⁸ [i]