MinT - Best Known (211−97, 211, s)-Nets in Base 3

Best Known (211−97, 211, s)-Nets in Base 3

(211−97, 211, 80)-Net over F₃ — Constructive and digital

Digital (114, 211, 80)-net over F₃, using

1 times m-reduction [i] based on digital (114, 212, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 106, 40)-net over F₉, using
  - net from sequence [i] based on digital (8, 39)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [i]

(211−97, 211, 133)-Net over F₃ — Digital

Digital (114, 211, 133)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(211−97, 211, 1099)-Net in Base 3 — Upper bound on s

There is no (114, 211, 1100)-net in base 3, because

1 times m-reduction [i] would yield (114, 210, 1100)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 16183 655284 066532 315591 643394 324674 126248 167152 881505 744420 849913 715716 327316 548761 313614 667837 751169 > 3²¹⁰ [i]