MinT - Best Known (213−89, 213, s)-Nets in Base 3

Best Known (213−89, 213, s)-Nets in Base 3

(213−89, 213, 148)-Net over F₃ — Constructive and digital

Digital (124, 213, 148)-net over F₃, using

1 times m-reduction [i] based on digital (124, 214, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 107, 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]

(213−89, 213, 175)-Net over F₃ — Digital

Digital (124, 213, 175)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(213−89, 213, 1673)-Net in Base 3 — Upper bound on s

There is no (124, 213, 1674)-net in base 3, because

1 times m-reduction [i] would yield (124, 212, 1674)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 141621 744370 706497 660318 312777 155097 819126 857267 084863 590864 777042 305608 250095 183012 522589 878580 541625 > 3²¹² [i]