MinT - Best Known (79, 79+47, s)-Nets in Base 8

Best Known (79, 79+47, s)-Nets in Base 8

(79, 79+47, 354)-Net over F₈ — Constructive and digital

Digital (79, 126, 354)-net over F₈, using

18 times m-reduction [i] based on digital (79, 144, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 72, 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]

(79, 79+47, 514)-Net in Base 8 — Constructive

(79, 126, 514)-net in base 8, using

trace code for nets [i] based on (16, 63, 257)-net in base 64, using
- 1 times m-reduction [i] based on (16, 64, 257)-net in base 64, using
  - base change [i] based on digital (0, 48, 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]

(79, 79+47, 787)-Net over F₈ — Digital

Digital (79, 126, 787)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(79, 79+47, 108993)-Net in Base 8 — Upper bound on s

There is no (79, 126, 108994)-net in base 8, because

1 times m-reduction [i] would yield (79, 125, 108994)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 76971 361090 791129 849135 976875 082364 900927 879100 426230 348395 810692 625914 732343 866556 594907 725775 924301 602288 114400 > 8¹²⁵ [i]