MinT - Best Known (105−25, 105, s)-Nets in Base 8

Best Known (105−25, 105, s)-Nets in Base 8

(105−25, 105, 708)-Net over F₈ — Constructive and digital

Digital (80, 105, 708)-net over F₈, using

1 times m-reduction [i] based on digital (80, 106, 708)-net over F₈, using
- (u,Â u+v)-construction [i] based on
  1. digital (27, 40, 354)-net over F₈, using
    - trace code for nets [i] based on digital (7, 20, 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]
  2. digital (40, 66, 354)-net over F₈, using
    - trace code for nets [i] based on digital (7, 33, 177)-net over F₆₄, using
      - net from sequence [i] based on digital (7, 176)-sequence over F₆₄ (see above)

(105−25, 105, 1032)-Net in Base 8 — Constructive

(80, 105, 1032)-net in base 8, using

8¹ times duplication [i] based on (79, 104, 1032)-net in base 8, using
- base change [i] based on digital (53, 78, 1032)-net over F₁₆, using
  - (u,Â u+v)-construction [i] based on
    1. digital (14, 26, 516)-net over F₁₆, using
      - trace code for nets [i] based on digital (1, 13, 258)-net over F₂₅₆, using
        net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
        Niederreiter sequence [i]
    2. digital (27, 52, 516)-net over F₁₆, using
      - trace code for nets [i] based on digital (1, 26, 258)-net over F₂₅₆, using
        net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆ (see above)

(105−25, 105, 12523)-Net over F₈ — Digital

Digital (80, 105, 12523)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(105−25, 105, large)-Net in Base 8 — Upper bound on s

There is no (80, 105, large)-net in base 8, because

23 times m-reduction [i] would yield (80, 82, large)-net in base 8, but
- mutually orthogonal hypercube bound [i]