MinT - Best Known (134−99, 134, s)-Nets in Base 8

Best Known (134−99, 134, s)-Nets in Base 8

(134−99, 134, 65)-Net over F₈ — Constructive and digital

Digital (35, 134, 65)-net over F₈, using

t-expansion [i] based on digital (14, 134, 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]

(134−99, 134, 112)-Net over F₈ — Digital

Digital (35, 134, 112)-net over F₈, using

net from sequence [i] based on digital (35, 111)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 35 and N(F) ≥ 112, using
  - a curve from the manYPoints database [i]

(134−99, 134, 741)-Net in Base 8 — Upper bound on s

There is no (35, 134, 742)-net in base 8, because

1 times m-reduction [i] would yield (35, 133, 742)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 368546 967161 729223 320808 452531 496392 422411 432728 919198 660279 738187 334210 790189 032981 274777 483402 142320 615821 810151 979036 > 8¹³³ [i]