MinT - Best Known (145−38, 145, s)-Nets in Base 8

Best Known (145−38, 145, s)-Nets in Base 8

(145−38, 145, 1026)-Net over F₈ — Constructive and digital

Digital (107, 145, 1026)-net over F₈, using

13 times m-reduction [i] based on digital (107, 158, 1026)-net over F₈, using
- trace code for nets [i] based on digital (28, 79, 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]

(145−38, 145, 7262)-Net over F₈ — Digital

Digital (107, 145, 7262)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(145−38, 145, large)-Net in Base 8 — Upper bound on s

There is no (107, 145, large)-net in base 8, because

36 times m-reduction [i] would yield (107, 109, large)-net in base 8, but
- mutually orthogonal hypercube bound [i]