MinT - Best Known (82, 82+26, s)-Nets in Base 8

Best Known (82, 82+26, s)-Nets in Base 8

(82, 82+26, 1026)-Net over F₈ — Constructive and digital

Digital (82, 108, 1026)-net over F₈, using

trace code for nets [i] based on digital (28, 54, 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]

(82, 82+26, 1030)-Net in Base 8 — Constructive

(82, 108, 1030)-net in base 8, using

base change [i] based on digital (55, 81, 1030)-net over F₁₆, using
- 1 times m-reduction [i] based on digital (55, 82, 1030)-net over F₁₆, using
  - (u,Â u+v)-construction [i] based on
    1. digital (13, 26, 514)-net over F₁₆, using
      - trace code for nets [i] based on digital (0, 13, 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 (29, 56, 516)-net over F₁₆, using
      - trace code for nets [i] based on digital (1, 28, 258)-net over F₂₅₆, using
        net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
        Niederreiter sequence [i]

(82, 82+26, 11597)-Net over F₈ — Digital

Digital (82, 108, 11597)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(82, 82+26, large)-Net in Base 8 — Upper bound on s

There is no (82, 108, large)-net in base 8, because

24 times m-reduction [i] would yield (82, 84, large)-net in base 8, but
- mutually orthogonal hypercube bound [i]