MinT - Best Known (85, 223, s)-Nets in Base 3

Best Known (85, 223, s)-Nets in Base 3

(85, 223, 60)-Net over F₃ — Constructive and digital

Digital (85, 223, 60)-net over F₃, using

net from sequence [i] based on digital (85, 59)-sequence over F₃, using
- base reduction for sequences [i] based on digital (13, 59)-sequence over F₉, using
  - s-reduction based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(85, 223, 84)-Net over F₃ — Digital

Digital (85, 223, 84)-net over F₃, using

t-expansion [i] based on digital (71, 223, 84)-net over F₃, using
- net from sequence [i] based on digital (71, 83)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 71 and N(F) ≥ 84, using
    - algebraic function fields over â„¤₃ by Niederreiter/Xing [i]

(85, 223, 397)-Net in Base 3 — Upper bound on s

There is no (85, 223, 398)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 27302 928254 900650 931765 758290 325417 397292 744165 294755 583530 757219 324003 940564 792749 727379 064612 871931 554101 > 3²²³ [i]