MinT - Best Known (142−63, 142, s)-Nets in Base 8

Best Known (142−63, 142, s)-Nets in Base 8

(142−63, 142, 354)-Net over F₈ — Constructive and digital

Digital (79, 142, 354)-net over F₈, using

2 times m-reduction [i] based on digital (79, 144, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 72, 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]

(142−63, 142, 383)-Net over F₈ — Digital

Digital (79, 142, 383)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(142−63, 142, 22707)-Net in Base 8 — Upper bound on s

There is no (79, 142, 22708)-net in base 8, because

1 times m-reduction [i] would yield (79, 141, 22708)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 21 680724 890081 911208 010175 765464 374208 179987 913764 796956 140719 701487 675628 053351 249131 497944 271603 243955 701612 363774 849946 610120 > 8¹⁴¹ [i]