MinT - Best Known (157−41, 157, s)-Nets in Base 8

Best Known (157−41, 157, s)-Nets in Base 8

(157−41, 157, 1026)-Net over F₈ — Constructive and digital

Digital (116, 157, 1026)-net over F₈, using

t-expansion [i] based on digital (114, 157, 1026)-net over F₈, using
- 15 times m-reduction [i] based on digital (114, 172, 1026)-net over F₈, using
  - trace code for nets [i] based on digital (28, 86, 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]

(157−41, 157, 7914)-Net over F₈ — Digital

Digital (116, 157, 7914)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(157−41, 157, large)-Net in Base 8 — Upper bound on s

There is no (116, 157, large)-net in base 8, because

39 times m-reduction [i] would yield (116, 118, large)-net in base 8, but
- mutually orthogonal hypercube bound [i]