MinT - Best Known (247−48, 247, s)-Nets in Base 3

Best Known (247−48, 247, s)-Nets in Base 3

(247−48, 247, 896)-Net over F₃ — Constructive and digital

Digital (199, 247, 896)-net over F₃, using

1 times m-reduction [i] based on digital (199, 248, 896)-net over F₃, using
- trace code for nets [i] based on digital (13, 62, 224)-net over F₈₁, using
  - net from sequence [i] based on digital (13, 223)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 13 and N(F) ≥ 224, using
      - a function field by SÃ©mirat [i]

(247−48, 247, 2978)-Net over F₃ — Digital

Digital (199, 247, 2978)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(247−48, 247, 398731)-Net in Base 3 — Upper bound on s

There is no (199, 247, 398732)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 7062 763788 168778 556996 595639 742991 761697 369228 778944 377155 725599 736164 962958 378637 242288 072328 748539 872505 994337 467969 > 3²⁴⁷ [i]