MinT - Best Known (66, 66+28, s)-Nets in Base 3

Best Known (66, 66+28, s)-Nets in Base 3

(66, 66+28, 156)-Net over F₃ — Constructive and digital

Digital (66, 94, 156)-net over F₃, using

3¹ times duplication [i] based on digital (65, 93, 156)-net over F₃, using
- trace code for nets [i] based on digital (3, 31, 52)-net over F₂₇, using
  - net from sequence [i] based on digital (3, 51)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 3 and N(F) ≥ 52, using
      - a function field by SÃ©mirat [i]

(66, 66+28, 248)-Net over F₃ — Digital

Digital (66, 94, 248)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(66, 66+28, 4816)-Net in Base 3 — Upper bound on s

There is no (66, 94, 4817)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 707 751707 073073 598593 164411 847890 400199 740569 > 3⁹⁴ [i]