MinT - Best Known (112−47, 112, s)-Nets in Base 8

Best Known (112−47, 112, s)-Nets in Base 8

(112−47, 112, 354)-Net over F₈ — Constructive and digital

Digital (65, 112, 354)-net over F₈, using

4 times m-reduction [i] based on digital (65, 116, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 58, 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]

(112−47, 112, 418)-Net over F₈ — Digital

Digital (65, 112, 418)-net over F₈, using

trace code for nets [i] based on digital (9, 56, 209)-net over F₆₄, using
- net from sequence [i] based on digital (9, 208)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 9 and N(F) ≥ 209, using
    - a curve from the manYPoints database [i]

(112−47, 112, 30728)-Net in Base 8 — Upper bound on s

There is no (65, 112, 30729)-net in base 8, because

1 times m-reduction [i] would yield (65, 111, 30729)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 17499 123299 779111 920391 481649 220499 602494 196811 972585 367206 600395 058054 840980 095591 490000 437517 614080 > 8¹¹¹ [i]