MinT - Best Known (74, 74+43, s)-Nets in Base 8

Best Known (74, 74+43, s)-Nets in Base 8

(74, 74+43, 354)-Net over F₈ — Constructive and digital

Digital (74, 117, 354)-net over F₈, using

17 times m-reduction [i] based on digital (74, 134, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 67, 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]

(74, 74+43, 514)-Net in Base 8 — Constructive

(74, 117, 514)-net in base 8, using

1 times m-reduction [i] based on (74, 118, 514)-net in base 8, using
- trace code for nets [i] based on (15, 59, 257)-net in base 64, using
  - 1 times m-reduction [i] based on (15, 60, 257)-net in base 64, using
    - base change [i] based on digital (0, 45, 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]

(74, 74+43, 794)-Net over F₈ — Digital

Digital (74, 117, 794)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(74, 74+43, 120738)-Net in Base 8 — Upper bound on s

There is no (74, 117, 120739)-net in base 8, because

1 times m-reduction [i] would yield (74, 116, 120739)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 573 450428 206247 486472 133077 571164 023263 573524 634361 956640 089609 157587 396321 209107 440633 976543 528425 524336 > 8¹¹⁶ [i]