MinT - Best Known (96−64, 96, s)-Nets in Base 9

Best Known (96−64, 96, s)-Nets in Base 9

(96−64, 96, 81)-Net over F₉ — Constructive and digital

Digital (32, 96, 81)-net over F₉, using

net from sequence [i] based on digital (32, 80)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 32 and N(F) ≥ 81, using
  - F₄ from the tower of function fields by Bezerra and GarcÃa over F₉ [i]

(96−64, 96, 120)-Net over F₉ — Digital

Digital (32, 96, 120)-net over F₉, using

t-expansion [i] based on digital (31, 96, 120)-net over F₉, using
- net from sequence [i] based on digital (31, 119)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 31 and N(F) ≥ 120, using
    - a curve from the manYPoints database [i]

(96−64, 96, 1146)-Net in Base 9 — Upper bound on s

There is no (32, 96, 1147)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 41 483871 879451 599195 401277 584015 615575 431884 603810 199533 046882 166304 733931 319828 563649 909505 > 9⁹⁶ [i]