MinT - Best Known (84, 133, s)-Nets in Base 8

Best Known (84, 133, s)-Nets in Base 8

(84, 133, 354)-Net over F₈ — Constructive and digital

Digital (84, 133, 354)-net over F₈, using

21 times m-reduction [i] based on digital (84, 154, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 77, 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]

(84, 133, 514)-Net in Base 8 — Constructive

(84, 133, 514)-net in base 8, using

1 times m-reduction [i] based on (84, 134, 514)-net in base 8, using
- trace code for nets [i] based on (17, 67, 257)-net in base 64, using
  - 1 times m-reduction [i] based on (17, 68, 257)-net in base 64, using
    - base change [i] based on digital (0, 51, 257)-net over F₂₅₆, using
      - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
        the rational function field F₂₅₆(x) [i]
        Niederreiter sequence [i]

(84, 133, 875)-Net over F₈ — Digital

Digital (84, 133, 875)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(84, 133, 129780)-Net in Base 8 — Upper bound on s

There is no (84, 133, 129781)-net in base 8, because

1 times m-reduction [i] would yield (84, 132, 129781)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 161403 490229 605209 667555 886055 964895 717170 519423 685094 485254 674287 269817 295861 894834 290250 982999 794905 478773 953044 007372 > 8¹³² [i]