MinT - Best Known (136−107, 136, s)-Nets in Base 8

Best Known (136−107, 136, s)-Nets in Base 8

(136−107, 136, 65)-Net over F₈ — Constructive and digital

Digital (29, 136, 65)-net over F₈, using

t-expansion [i] based on digital (14, 136, 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]

(136−107, 136, 97)-Net over F₈ — Digital

Digital (29, 136, 97)-net over F₈, using

t-expansion [i] based on digital (28, 136, 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]

(136−107, 136, 554)-Net in Base 8 — Upper bound on s

There is no (29, 136, 555)-net in base 8, because

1 times m-reduction [i] would yield (29, 135, 555)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 86 377749 234622 999451 308275 256535 045643 367695 698845 016012 530408 367935 529696 460872 206718 419788 843447 015695 610244 009503 832192 > 8¹³⁵ [i]