MinT - Best Known (152−57, 152, s)-Nets in Base 8

Best Known (152−57, 152, s)-Nets in Base 8

(152−57, 152, 354)-Net over F₈ — Constructive and digital

Digital (95, 152, 354)-net over F₈, using

t-expansion [i] based on digital (93, 152, 354)-net over F₈, using
- 20 times m-reduction [i] based on digital (93, 172, 354)-net over F₈, using
  - trace code for nets [i] based on digital (7, 86, 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]

(152−57, 152, 514)-Net in Base 8 — Constructive

(95, 152, 514)-net in base 8, using

base change [i] based on digital (57, 114, 514)-net over F₁₆, using
- trace code for nets [i] based on digital (0, 57, 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]

(152−57, 152, 889)-Net over F₈ — Digital

Digital (95, 152, 889)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(152−57, 152, 119695)-Net in Base 8 — Upper bound on s

There is no (95, 152, 119696)-net in base 8, because

1 times m-reduction [i] would yield (95, 151, 119696)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 23260 112363 248361 274036 607447 499602 881544 346437 317251 229889 194134 290036 806968 439936 199602 701169 653457 855485 595032 471546 333425 106197 305384 > 8¹⁵¹ [i]