MinT - Best Known (85, 85+28, s)-Nets in Base 8

Best Known (85, 85+28, s)-Nets in Base 8

(85, 85+28, 1026)-Net over F₈ — Constructive and digital

Digital (85, 113, 1026)-net over F₈, using

1 times m-reduction [i] based on digital (85, 114, 1026)-net over F₈, using
- trace code for nets [i] based on digital (28, 57, 513)-net over F₆₄, using
  - net from sequence [i] based on digital (28, 512)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
      - the Hermitian function field over F₆₄ [i]

(85, 85+28, 1028)-Net in Base 8 — Constructive

(85, 113, 1028)-net in base 8, using

8¹ times duplication [i] based on (84, 112, 1028)-net in base 8, using
- base change [i] based on digital (56, 84, 1028)-net over F₁₆, using
  - (u,Â u+v)-construction [i] based on
    1. digital (14, 28, 514)-net over F₁₆, using
      - trace code for nets [i] based on digital (0, 14, 257)-net over F₂₅₆, using
        net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
        the rational function field F₂₅₆(x) [i]
        Niederreiter sequence [i]
    2. digital (28, 56, 514)-net over F₁₆, using
      - trace code for nets [i] based on digital (0, 28, 257)-net over F₂₅₆, using
        net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆ (see above)

(85, 85+28, 9409)-Net over F₈ — Digital

Digital (85, 113, 9409)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(85, 85+28, large)-Net in Base 8 — Upper bound on s

There is no (85, 113, large)-net in base 8, because

26 times m-reduction [i] would yield (85, 87, large)-net in base 8, but
- mutually orthogonal hypercube bound [i]