MinT - Best Known (149−57, 149, s)-Nets in Base 8

Best Known (149−57, 149, s)-Nets in Base 8

(149−57, 149, 354)-Net over F₈ — Constructive and digital

Digital (92, 149, 354)-net over F₈, using

21 times m-reduction [i] based on digital (92, 170, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 85, 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]

(149−57, 149, 432)-Net in Base 8 — Constructive

(92, 149, 432)-net in base 8, using

3 times m-reduction [i] based on (92, 152, 432)-net in base 8, using
- trace code for nets [i] based on (16, 76, 216)-net in base 64, using
  - 1 times m-reduction [i] based on (16, 77, 216)-net in base 64, using
    - base change [i] based on digital (5, 66, 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]

(149−57, 149, 791)-Net over F₈ — Digital

Digital (92, 149, 791)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(149−57, 149, 95786)-Net in Base 8 — Upper bound on s

There is no (92, 149, 95787)-net in base 8, because

1 times m-reduction [i] would yield (92, 148, 95787)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 45 436996 470509 957182 298462 545436 719299 269293 363391 584714 487314 590705 899757 616789 287087 800380 939089 254899 119172 349475 443795 657316 691800 > 8¹⁴⁸ [i]