MinT - Best Known (235−121, 235, s)-Nets in Base 3

Best Known (235−121, 235, s)-Nets in Base 3

(235−121, 235, 74)-Net over F₃ — Constructive and digital

Digital (114, 235, 74)-net over F₃, using

t-expansion [i] based on digital (107, 235, 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]

(235−121, 235, 120)-Net over F₃ — Digital

Digital (114, 235, 120)-net over F₃, using

t-expansion [i] based on digital (113, 235, 120)-net over F₃, using
- net from sequence [i] based on digital (113, 119)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 113 and N(F) ≥ 120, using
    - algebraic function fields over â„¤₃ by Niederreiter/Xing [i]

(235−121, 235, 783)-Net in Base 3 — Upper bound on s

There is no (114, 235, 784)-net in base 3, because

1 times m-reduction [i] would yield (114, 234, 784)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4513 887980 239300 269054 258242 706653 703868 232506 840574 552699 146864 203027 446547 497606 845020 358647 469099 333328 385921 > 3²³⁴ [i]