MinT - Best Known (156−67, 156, s)-Nets in Base 8

Best Known (156−67, 156, s)-Nets in Base 8

(156−67, 156, 354)-Net over F₈ — Constructive and digital

Digital (89, 156, 354)-net over F₈, using

8 times m-reduction [i] based on digital (89, 164, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 82, 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]

(156−67, 156, 478)-Net over F₈ — Digital

Digital (89, 156, 478)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(156−67, 156, 32792)-Net in Base 8 — Upper bound on s

There is no (89, 156, 32793)-net in base 8, because

1 times m-reduction [i] would yield (89, 155, 32793)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 95 362105 034544 847410 311474 879610 528737 339284 039956 880892 721506 660166 021729 495820 059739 097102 007669 865205 021361 670145 950052 148658 522321 141760 > 8¹⁵⁵ [i]