MinT - Best Known (211−66, 211, s)-Nets in Base 3

Best Known (211−66, 211, s)-Nets in Base 3

(211−66, 211, 192)-Net over F₃ — Constructive and digital

Digital (145, 211, 192)-net over F₃, using

3¹ times duplication [i] based on digital (144, 210, 192)-net over F₃, using
- trace code for nets [i] based on digital (4, 70, 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]

(211−66, 211, 407)-Net over F₃ — Digital

Digital (145, 211, 407)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(211−66, 211, 7363)-Net in Base 3 — Upper bound on s

There is no (145, 211, 7364)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 47103 749096 538227 290850 830522 797983 898661 087632 988757 505967 074892 457130 523566 488422 306992 351690 005385 > 3²¹¹ [i]