MinT - Best Known (204−83, 204, s)-Nets in Base 3

Best Known (204−83, 204, s)-Nets in Base 3

(204−83, 204, 148)-Net over F₃ — Constructive and digital

Digital (121, 204, 148)-net over F₃, using

4 times m-reduction [i] based on digital (121, 208, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 104, 74)-net over F₉, using
  - net from sequence [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]

(204−83, 204, 181)-Net over F₃ — Digital

Digital (121, 204, 181)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(204−83, 204, 1818)-Net in Base 3 — Upper bound on s

There is no (121, 204, 1819)-net in base 3, because

1 times m-reduction [i] would yield (121, 203, 1819)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 7 237010 990157 203190 481702 487439 521734 634086 473292 782171 234055 854508 337118 505473 091703 300780 762535 > 3²⁰³ [i]