MinT - Best Known (80, 133, s)-Nets in Base 8

Best Known (80, 133, s)-Nets in Base 8

(80, 133, 354)-Net over F₈ — Constructive and digital

Digital (80, 133, 354)-net over F₈, using

13 times m-reduction [i] based on digital (80, 146, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 73, 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]

(80, 133, 384)-Net in Base 8 — Constructive

(80, 133, 384)-net in base 8, using

1 times m-reduction [i] based on (80, 134, 384)-net in base 8, using
- trace code for nets [i] based on (13, 67, 192)-net in base 64, using
  - 3 times m-reduction [i] based on (13, 70, 192)-net in base 64, using
    - base change [i] based on digital (3, 60, 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]

(80, 133, 590)-Net over F₈ — Digital

Digital (80, 133, 590)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(80, 133, 57941)-Net in Base 8 — Upper bound on s

There is no (80, 133, 57942)-net in base 8, because

1 times m-reduction [i] would yield (80, 132, 57942)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 161405 988033 195900 047076 128676 202172 203558 089630 429399 606218 559359 317431 369535 987552 253147 740666 140806 060357 795055 013840 > 8¹³² [i]