MinT - Best Known (142−62, 142, s)-Nets in Base 8

Best Known (142−62, 142, s)-Nets in Base 8

(142−62, 142, 354)-Net over F₈ — Constructive and digital

Digital (80, 142, 354)-net over F₈, using

4 times m-reduction [i] based on digital (80, 146, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 73, 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]

(142−62, 142, 418)-Net over F₈ — Digital

Digital (80, 142, 418)-net over F₈, using

trace code for nets [i] based on digital (9, 71, 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]

(142−62, 142, 24284)-Net in Base 8 — Upper bound on s

There is no (80, 142, 24285)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 173 485302 007145 782803 612099 739417 635385 237009 543335 618607 618856 925462 748809 347893 433627 930636 324866 947272 702680 479700 095354 297920 > 8¹⁴² [i]