MinT - Best Known (205−64, 205, s)-Nets in Base 3

Best Known (205−64, 205, s)-Nets in Base 3

(205−64, 205, 192)-Net over F₃ — Constructive and digital

Digital (141, 205, 192)-net over F₃, using

3¹ times duplication [i] based on digital (140, 204, 192)-net over F₃, using
- trace code for nets [i] based on digital (4, 68, 64)-net over F₂₇, using
  - net from sequence [i] based on digital (4, 63)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
      - a function field by SÃ©mirat [i]

(205−64, 205, 400)-Net over F₃ — Digital

Digital (141, 205, 400)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(205−64, 205, 7253)-Net in Base 3 — Upper bound on s

There is no (141, 205, 7254)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 64 770823 655705 393376 893929 659014 665492 775442 957600 688846 599241 382504 995909 285864 380583 933387 892033 > 3²⁰⁵ [i]