MinT - Best Known (129−33, 129, s)-Nets in Base 8

Best Known (129−33, 129, s)-Nets in Base 8

(129−33, 129, 1026)-Net over F₈ — Constructive and digital

Digital (96, 129, 1026)-net over F₈, using

7 times m-reduction [i] based on digital (96, 136, 1026)-net over F₈, using
- trace code for nets [i] based on digital (28, 68, 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]

(129−33, 129, 8002)-Net over F₈ — Digital

Digital (96, 129, 8002)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(129−33, 129, large)-Net in Base 8 — Upper bound on s

There is no (96, 129, large)-net in base 8, because

31 times m-reduction [i] would yield (96, 98, large)-net in base 8, but
- mutually orthogonal hypercube bound [i]