MinT - Best Known (110, 110+129, s)-Nets in Base 3

Best Known (110, 110+129, s)-Nets in Base 3

(110, 110+129, 74)-Net over F₃ — Constructive and digital

Digital (110, 239, 74)-net over F₃, using

t-expansion [i] based on digital (107, 239, 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]

(110, 110+129, 104)-Net over F₃ — Digital

Digital (110, 239, 104)-net over F₃, using

t-expansion [i] based on digital (102, 239, 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]

(110, 110+129, 672)-Net in Base 3 — Upper bound on s

There is no (110, 239, 673)-net in base 3, because

1 times m-reduction [i] would yield (110, 238, 673)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 379306 887526 669248 837383 079302 851295 177972 465508 881079 178808 978574 270215 427428 723524 958266 930241 148604 640929 979649 > 3²³⁸ [i]