MinT - Best Known (209−112, 209, s)-Nets in Base 3

Best Known (209−112, 209, s)-Nets in Base 3

(209−112, 209, 64)-Net over F₃ — Constructive and digital

Digital (97, 209, 64)-net over F₃, using

t-expansion [i] based on digital (89, 209, 64)-net over F₃, using
- net from sequence [i] based on digital (89, 63)-sequence over F₃, using
  - base reduction for sequences [i] 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]

(209−112, 209, 96)-Net over F₃ — Digital

Digital (97, 209, 96)-net over F₃, using

t-expansion [i] based on digital (89, 209, 96)-net over F₃, using
- net from sequence [i] based on digital (89, 95)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 89 and N(F) ≥ 96, using
    - algebraic function fields over â„¤₃ by Niederreiter/Xing [i]

(209−112, 209, 601)-Net in Base 3 — Upper bound on s

There is no (97, 209, 602)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 5478 296610 123224 495425 252954 940831 800376 140451 779526 271753 088329 772333 341406 980887 166924 091148 448945 > 3²⁰⁹ [i]