MinT - Best Known (234−134, 234, s)-Nets in Base 3

Best Known (234−134, 234, s)-Nets in Base 3

(234−134, 234, 67)-Net over F₃ — Constructive and digital

Digital (100, 234, 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]

(234−134, 234, 96)-Net over F₃ — Digital

Digital (100, 234, 96)-net over F₃, using

t-expansion [i] based on digital (89, 234, 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]

(234−134, 234, 534)-Net in Base 3 — Upper bound on s

There is no (100, 234, 535)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4732 958684 508580 209852 830591 311653 741236 217819 579123 117172 681989 945880 150620 098448 347387 347027 690545 202149 200091 > 3²³⁴ [i]