MinT - Best Known (123, 123+83, s)-Nets in Base 3

Best Known (123, 123+83, s)-Nets in Base 3

(123, 123+83, 148)-Net over F₃ — Constructive and digital

Digital (123, 206, 148)-net over F₃, using

6 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+83, 188)-Net over F₃ — Digital

Digital (123, 206, 188)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(123, 123+83, 1920)-Net in Base 3 — Upper bound on s

There is no (123, 206, 1921)-net in base 3, because

1 times m-reduction [i] would yield (123, 205, 1921)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 64 682634 001159 089770 927751 953628 988907 890040 343082 797859 113956 259433 077411 271478 580386 721610 964835 > 3²⁰⁵ [i]