MinT - Best Known (120−96, 120, s)-Nets in Base 8

Best Known (120−96, 120, s)-Nets in Base 8

(120−96, 120, 65)-Net over F₈ — Constructive and digital

Digital (24, 120, 65)-net over F₈, using

t-expansion [i] based on digital (14, 120, 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]

(120−96, 120, 81)-Net over F₈ — Digital

Digital (24, 120, 81)-net over F₈, using

net from sequence [i] based on digital (24, 80)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 24 and N(F) ≥ 81, using
  - a curve from the manYPoints database [i]

(120−96, 120, 454)-Net in Base 8 — Upper bound on s

There is no (24, 120, 455)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2 385298 097153 657685 596935 582949 896147 263594 568252 721839 774287 183154 512869 062415 879820 481526 917135 817209 970244 > 8¹²⁰ [i]