MinT - Best Known (123, 123+80, s)-Nets in Base 3

Best Known (123, 123+80, s)-Nets in Base 3

(123, 123+80, 148)-Net over F₃ — Constructive and digital

Digital (123, 203, 148)-net over F₃, using

9 times m-reduction [i] based on digital (123, 212, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 106, 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]

(123, 123+80, 197)-Net over F₃ — Digital

Digital (123, 203, 197)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(123, 123+80, 2041)-Net in Base 3 — Upper bound on s

There is no (123, 203, 2042)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 7 278235 788262 926310 003123 150360 235462 139988 311293 197823 625331 719840 952104 585499 003936 355775 900945 > 3²⁰³ [i]