MinT - Best Known (81−56, 81, s)-Nets in Base 8

Best Known (81−56, 81, s)-Nets in Base 8

(81−56, 81, 65)-Net over F₈ — Constructive and digital

Digital (25, 81, 65)-net over F₈, using

t-expansion [i] based on digital (14, 81, 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]

(81−56, 81, 86)-Net over F₈ — Digital

Digital (25, 81, 86)-net over F₈, using

net from sequence [i] based on digital (25, 85)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 25 and N(F) ≥ 86, using
  - a curve from the manYPoints database [i]

(81−56, 81, 643)-Net in Base 8 — Upper bound on s

There is no (25, 81, 644)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 14 152912 262726 462025 352578 728020 598165 917083 459270 430999 021998 504808 961760 > 8⁸¹ [i]