MinT - Best Known (140−106, 140, s)-Nets in Base 8

Best Known (140−106, 140, s)-Nets in Base 8

(140−106, 140, 65)-Net over F₈ — Constructive and digital

Digital (34, 140, 65)-net over F₈, using

t-expansion [i] based on digital (14, 140, 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]

(140−106, 140, 98)-Net over F₈ — Digital

Digital (34, 140, 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]

(140−106, 140, 681)-Net in Base 8 — Upper bound on s

There is no (34, 140, 682)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2 759239 409531 150235 592221 815633 817314 343816 866919 159143 198637 762903 812309 929110 062640 324331 061356 480343 416368 132711 595256 937552 > 8¹⁴⁰ [i]