MinT - Best Known (69, 69+27, s)-Nets in Base 3

Best Known (69, 69+27, s)-Nets in Base 3

(69, 69+27, 204)-Net over F₃ — Constructive and digital

Digital (69, 96, 204)-net over F₃, using

trace code for nets [i] based on digital (5, 32, 68)-net over F₂₇, using
- net from sequence [i] based on digital (5, 67)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 5 and N(F) ≥ 68, using
    - a function field by SÃ©mirat [i]

(69, 69+27, 311)-Net over F₃ — Digital

Digital (69, 96, 311)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(69, 69+27, 8677)-Net in Base 3 — Upper bound on s

There is no (69, 96, 8678)-net in base 3, because

1 times m-reduction [i] would yield (69, 95, 8678)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2121 713136 250620 586580 996482 539781 613959 755669 > 3⁹⁵ [i]