MinT - Best Known (89−41, 89, s)-Nets in Base 8

Best Known (89−41, 89, s)-Nets in Base 8

(89−41, 89, 208)-Net over F₈ — Constructive and digital

Digital (48, 89, 208)-net over F₈, using

1 times m-reduction [i] based on digital (48, 90, 208)-net over F₈, using
- trace code for nets [i] based on digital (3, 45, 104)-net over F₆₄, using
  - net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
      - a function field by SÃ©mirat [i]

(89−41, 89, 226)-Net over F₈ — Digital

Digital (48, 89, 226)-net over F₈, using

1 times m-reduction [i] based on digital (48, 90, 226)-net over F₈, using
- trace code for nets [i] based on digital (3, 45, 113)-net over F₆₄, using
  - net from sequence [i] based on digital (3, 112)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 113, using
      - a curve from the manYPoints database [i]

(89−41, 89, 11151)-Net in Base 8 — Upper bound on s

There is no (48, 89, 11152)-net in base 8, because

1 times m-reduction [i] would yield (48, 88, 11152)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 29 682965 220833 456972 602677 844822 610868 560532 633442 351544 066745 574403 993517 670936 > 8⁸⁸ [i]