MinT - Best Known (211−64, 211, s)-Nets in Base 3

Best Known (211−64, 211, s)-Nets in Base 3

(211−64, 211, 228)-Net over F₃ — Constructive and digital

Digital (147, 211, 228)-net over F₃, using

3¹ times duplication [i] based on digital (146, 210, 228)-net over F₃, using
- trace code for nets [i] based on digital (6, 70, 76)-net over F₂₇, using
  - net from sequence [i] based on digital (6, 75)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 6 and N(F) ≥ 76, using
      - a function field by SÃ©mirat [i]

(211−64, 211, 448)-Net over F₃ — Digital

Digital (147, 211, 448)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(211−64, 211, 8919)-Net in Base 3 — Upper bound on s

There is no (147, 211, 8920)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 47139 227138 829129 309147 575456 828977 747787 948143 525027 916957 550270 453499 217666 550863 106465 486470 150145 > 3²¹¹ [i]