MinT - Best Known (230−123, 230, s)-Nets in Base 3

Best Known (230−123, 230, s)-Nets in Base 3

(230−123, 230, 74)-Net over F₃ — Constructive and digital

Digital (107, 230, 74)-net over F₃, using

net from sequence [i] based on digital (107, 73)-sequence over F₃, using
- base reduction for sequences [i] 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]

(230−123, 230, 104)-Net over F₃ — Digital

Digital (107, 230, 104)-net over F₃, using

t-expansion [i] based on digital (102, 230, 104)-net over F₃, using
- net from sequence [i] based on digital (102, 103)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 102 and N(F) ≥ 104, using
    - algebraic function fields over â„¤₃ by Niederreiter/Xing [i]

(230−123, 230, 669)-Net in Base 3 — Upper bound on s

There is no (107, 230, 670)-net in base 3, because

1 times m-reduction [i] would yield (107, 229, 670)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 18 425866 989709 706244 853772 903116 431119 166471 229612 511289 776626 812737 001392 258999 627649 041419 724730 113342 267877 > 3²²⁹ [i]