MinT - Best Known (54, 84, s)-Nets in Base 8

Best Known (54, 84, s)-Nets in Base 8

(54, 84, 354)-Net over F₈ — Constructive and digital

Digital (54, 84, 354)-net over F₈, using

10 times m-reduction [i] based on digital (54, 94, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 47, 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]

(54, 84, 516)-Net in Base 8 — Constructive

(54, 84, 516)-net in base 8, using

base change [i] based on digital (33, 63, 516)-net over F₁₆, using
- 1 times m-reduction [i] based on digital (33, 64, 516)-net over F₁₆, using
  - trace code for nets [i] based on digital (1, 32, 258)-net over F₂₅₆, using
    - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]

(54, 84, 703)-Net over F₈ — Digital

Digital (54, 84, 703)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(54, 84, 104697)-Net in Base 8 — Upper bound on s

There is no (54, 84, 104698)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 7237 950535 779983 650586 116374 830591 273044 902281 604752 247597 444986 662946 820856 > 8⁸⁴ [i]