MinT - Best Known (69, 69+29, s)-Nets in Base 3

Best Known (69, 69+29, s)-Nets in Base 3

(69, 69+29, 156)-Net over F₃ — Constructive and digital

Digital (69, 98, 156)-net over F₃, using

1 times m-reduction [i] based on digital (69, 99, 156)-net over F₃, using
- trace code for nets [i] based on digital (3, 33, 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]

(69, 69+29, 262)-Net over F₃ — Digital

Digital (69, 98, 262)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(69, 69+29, 6098)-Net in Base 3 — Upper bound on s

There is no (69, 98, 6099)-net in base 3, because

1 times m-reduction [i] would yield (69, 97, 6099)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 19101 320112 506533 996538 575702 504231 160794 273133 > 3⁹⁷ [i]