MinT - Best Known (143−52, 143, s)-Nets in Base 8

Best Known (143−52, 143, s)-Nets in Base 8

(143−52, 143, 354)-Net over F₈ — Constructive and digital

Digital (91, 143, 354)-net over F₈, using

25 times m-reduction [i] based on digital (91, 168, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 84, 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]

(143−52, 143, 516)-Net in Base 8 — Constructive

(91, 143, 516)-net in base 8, using

1 times m-reduction [i] based on (91, 144, 516)-net in base 8, using
- base change [i] based on digital (55, 108, 516)-net over F₁₆, using
  - trace code for nets [i] based on digital (1, 54, 258)-net over F₂₅₆, using
    - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]

(143−52, 143, 991)-Net over F₈ — Digital

Digital (91, 143, 991)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(143−52, 143, 139681)-Net in Base 8 — Upper bound on s

There is no (91, 143, 139682)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1386 411618 157083 439043 666931 059582 942146 247752 239288 733843 290391 715642 816634 233528 415496 029055 322649 943712 596910 232207 435639 617200 > 8¹⁴³ [i]