MinT - Best Known (35, 35+123, s)-Nets in Base 8

Best Known (35, 35+123, s)-Nets in Base 8

(35, 35+123, 65)-Net over F₈ — Constructive and digital

Digital (35, 158, 65)-net over F₈, using

t-expansion [i] based on digital (14, 158, 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]

(35, 35+123, 112)-Net over F₈ — Digital

Digital (35, 158, 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]

(35, 35+123, 672)-Net in Base 8 — Upper bound on s

There is no (35, 158, 673)-net in base 8, because

1 times m-reduction [i] would yield (35, 157, 673)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 6499 637401 863302 349865 911937 975707 646907 672490 603829 558535 669058 303152 076450 675814 947548 344049 223308 699844 639634 688309 647830 964116 157214 909312 > 8¹⁵⁷ [i]