MinT - Best Known (110−76, 110, s)-Nets in Base 8

Best Known (110−76, 110, s)-Nets in Base 8

(110−76, 110, 65)-Net over F₈ — Constructive and digital

Digital (34, 110, 65)-net over F₈, using

t-expansion [i] based on digital (14, 110, 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]

(110−76, 110, 98)-Net over F₈ — Digital

Digital (34, 110, 98)-net over F₈, using

net from sequence [i] based on digital (34, 97)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 34 and N(F) ≥ 98, using
  - a curve from the manYPoints database [i]

(110−76, 110, 859)-Net in Base 8 — Upper bound on s

There is no (34, 110, 860)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2266 749169 568452 958850 333611 037130 865341 481884 300723 844275 188691 315432 571707 007969 472771 049089 510276 > 8¹¹⁰ [i]