MinT - Best Known (128, 206, s)-Nets in Base 3

Best Known (128, 206, s)-Nets in Base 3

(128, 206, 156)-Net over F₃ — Constructive and digital

Digital (128, 206, 156)-net over F₃, using

6 times m-reduction [i] based on digital (128, 212, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 106, 78)-net over F₉, using
  - net from sequence [i] based on digital (22, 77)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
      - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(128, 206, 225)-Net over F₃ — Digital

Digital (128, 206, 225)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(128, 206, 2511)-Net in Base 3 — Upper bound on s

There is no (128, 206, 2512)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 193 809103 081686 729991 817323 618316 097895 197374 885289 972487 279917 909733 578483 994904 542718 930852 190657 > 3²⁰⁶ [i]