MinT - Best Known (192−112, 192, s)-Nets in Base 3

Best Known (192−112, 192, s)-Nets in Base 3

(192−112, 192, 55)-Net over F₃ — Constructive and digital

Digital (80, 192, 55)-net over F₃, using

net from sequence [i] based on digital (80, 54)-sequence over F₃, using
- base reduction for sequences [i] based on digital (13, 54)-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]

(192−112, 192, 84)-Net over F₃ — Digital

Digital (80, 192, 84)-net over F₃, using

t-expansion [i] based on digital (71, 192, 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]

(192−112, 192, 416)-Net in Base 3 — Upper bound on s

There is no (80, 192, 417)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 43 634231 599916 816775 931319 302628 433666 512334 513129 497565 988587 792317 109897 419066 420558 567265 > 3¹⁹² [i]