MinT - Best Known (139−35, 139, s)-Nets in Base 8

Best Known (139−35, 139, s)-Nets in Base 8

(139−35, 139, 1026)-Net over F₈ — Constructive and digital

Digital (104, 139, 1026)-net over F₈, using

13 times m-reduction [i] based on digital (104, 152, 1026)-net over F₈, using
- trace code for nets [i] based on digital (28, 76, 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]

(139−35, 139, 9532)-Net over F₈ — Digital

Digital (104, 139, 9532)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(139−35, 139, large)-Net in Base 8 — Upper bound on s

There is no (104, 139, large)-net in base 8, because

33 times m-reduction [i] would yield (104, 106, large)-net in base 8, but
- mutually orthogonal hypercube bound [i]