MinT - Best Known (144−59, 144, s)-Nets in Base 8

Best Known (144−59, 144, s)-Nets in Base 8

(144−59, 144, 354)-Net over F₈ — Constructive and digital

Digital (85, 144, 354)-net over F₈, using

12 times m-reduction [i] based on digital (85, 156, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 78, 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]

(144−59, 144, 552)-Net over F₈ — Digital

Digital (85, 144, 552)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(144−59, 144, 47317)-Net in Base 8 — Upper bound on s

There is no (85, 144, 47318)-net in base 8, because

1 times m-reduction [i] would yield (85, 143, 47318)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1386 426696 150784 819277 217279 322346 832369 984380 613443 217616 580801 432511 564880 323345 410971 283963 206480 951319 791799 019303 392085 998968 > 8¹⁴³ [i]