MinT - Best Known (156−127, 156, s)-Nets in Base 8

Best Known (156−127, 156, s)-Nets in Base 8

(156−127, 156, 65)-Net over F₈ — Constructive and digital

Digital (29, 156, 65)-net over F₈, using

t-expansion [i] based on digital (14, 156, 65)-net over F₈, using
- net from sequence [i] based on digital (14, 64)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
    - the Suzuki function field over F₈ [i]

(156−127, 156, 97)-Net over F₈ — Digital

Digital (29, 156, 97)-net over F₈, using

t-expansion [i] based on digital (28, 156, 97)-net over F₈, using
- net from sequence [i] based on digital (28, 96)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 28 and N(F) ≥ 97, using
    - a curve from the manYPoints database [i]

(156−127, 156, 539)-Net in Base 8 — Upper bound on s

There is no (29, 156, 540)-net in base 8, because

1 times m-reduction [i] would yield (29, 155, 540)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 100 356160 637961 822631 163257 026477 905460 736810 815416 792716 130426 872923 873895 211720 426026 175038 124139 920802 593134 868310 460417 596301 285084 264832 > 8¹⁵⁵ [i]