MinT - Best Known (59, 59+35, s)-Nets in Base 8

Best Known (59, 59+35, s)-Nets in Base 8

(59, 59+35, 354)-Net over F₈ — Constructive and digital

Digital (59, 94, 354)-net over F₈, using

10 times m-reduction [i] based on digital (59, 104, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 52, 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]

(59, 59+35, 514)-Net in Base 8 — Constructive

(59, 94, 514)-net in base 8, using

trace code for nets [i] based on (12, 47, 257)-net in base 64, using
- 1 times m-reduction [i] based on (12, 48, 257)-net in base 64, using
  - base change [i] based on digital (0, 36, 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]

(59, 59+35, 624)-Net over F₈ — Digital

Digital (59, 94, 624)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(59, 59+35, 89377)-Net in Base 8 — Upper bound on s

There is no (59, 94, 89378)-net in base 8, because

1 times m-reduction [i] would yield (59, 93, 89378)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 971360 136921 302704 795738 430211 505905 706890 743130 527564 630656 680506 557089 322190 648074 > 8⁹³ [i]