MinT - Best Known (210−110, 210, s)-Nets in Base 3

Best Known (210−110, 210, s)-Nets in Base 3

(210−110, 210, 67)-Net over F₃ — Constructive and digital

Digital (100, 210, 67)-net over F₃, using

net from sequence [i] based on digital (100, 66)-sequence over F₃, using
- base reduction for sequences [i] based on digital (17, 66)-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]

(210−110, 210, 96)-Net over F₃ — Digital

Digital (100, 210, 96)-net over F₃, using

t-expansion [i] based on digital (89, 210, 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]

(210−110, 210, 654)-Net in Base 3 — Upper bound on s

There is no (100, 210, 655)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 15804 324463 290310 153343 015669 436769 057909 579265 212877 300762 667579 727308 081784 395656 447611 004712 392403 > 3²¹⁰ [i]