MinT - Best Known (66, 66+27, s)-Nets in Base 3

Best Known (66, 66+27, s)-Nets in Base 3

(66, 66+27, 192)-Net over F₃ — Constructive and digital

Digital (66, 93, 192)-net over F₃, using

trace code for nets [i] based on digital (4, 31, 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]

(66, 66+27, 270)-Net over F₃ — Digital

Digital (66, 93, 270)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(66, 66+27, 6731)-Net in Base 3 — Upper bound on s

There is no (66, 93, 6732)-net in base 3, because

1 times m-reduction [i] would yield (66, 92, 6732)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 78 604674 307925 627348 457366 629130 168101 826681 > 3⁹² [i]