MinT - Best Known (101, 101+138, s)-Nets in Base 3

Best Known (101, 101+138, s)-Nets in Base 3

(101, 101+138, 68)-Net over F₃ — Constructive and digital

Digital (101, 239, 68)-net over F₃, using

net from sequence [i] based on digital (101, 67)-sequence over F₃, using
- base reduction for sequences [i] based on digital (17, 67)-sequence over F₉, using
  - s-reduction based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

(101, 101+138, 96)-Net over F₃ — Digital

Digital (101, 239, 96)-net over F₃, using

t-expansion [i] based on digital (89, 239, 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]

(101, 101+138, 530)-Net in Base 3 — Upper bound on s

There is no (101, 239, 531)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 123718 222288 981142 753863 853281 070790 360515 159944 857629 675450 059857 178615 206999 108991 696588 593711 747432 550322 715551 > 3²³⁹ [i]